Concise Bible Dictionary:

There are two applications of this word, one of which is apt to be overlooked. The one is the confession of sin. This was enjoined by the law, and if accompanied with a sacrifice it led to forgiveness (Lev. 5:55And it shall be, when he shall be guilty in one of these things, that he shall confess that he hath sinned in that thing: (Leviticus 5:5); Num. 5:77Then they shall confess their sin which they have done: and he shall recompense his trespass with the principal thereof, and add unto it the fifth part thereof, and give it unto him against whom he hath trespassed. (Numbers 5:7)). It is beautiful to see how Ezra, Nehemiah, and Daniel confessed the sins of the people as if they had been their own (Ezra 9:1-151Now when these things were done, the princes came to me, saying, The people of Israel, and the priests, and the Levites, have not separated themselves from the people of the lands, doing according to their abominations, even of the Canaanites, the Hittites, the Perizzites, the Jebusites, the Ammonites, the Moabites, the Egyptians, and the Amorites. 2For they have taken of their daughters for themselves, and for their sons: so that the holy seed have mingled themselves with the people of those lands: yea, the hand of the princes and rulers hath been chief in this trespass. 3And when I heard this thing, I rent my garment and my mantle, and plucked off the hair of my head and of my beard, and sat down astonied. 4Then were assembled unto me every one that trembled at the words of the God of Israel, because of the transgression of those that had been carried away; and I sat astonied until the evening sacrifice. 5And at the evening sacrifice I arose up from my heaviness; and having rent my garment and my mantle, I fell upon my knees, and spread out my hands unto the Lord my God, 6And said, O my God, I am ashamed and blush to lift up my face to thee, my God: for our iniquities are increased over our head, and our trespass is grown up unto the heavens. 7Since the days of our fathers have we been in a great trespass unto this day; and for our iniquities have we, our kings, and our priests, been delivered into the hand of the kings of the lands, to the sword, to captivity, and to a spoil, and to confusion of face, as it is this day. 8And now for a little space grace hath been showed from the Lord our God, to leave us a remnant to escape, and to give us a nail in his holy place, that our God may lighten our eyes, and give us a little reviving in our bondage. 9For we were bondmen; yet our God hath not forsaken us in our bondage, but hath extended mercy unto us in the sight of the kings of Persia, to give us a reviving, to set up the house of our God, and to repair the desolations thereof, and to give us a wall in Judah and in Jerusalem. 10And now, O our God, what shall we say after this? for we have forsaken thy commandments, 11Which thou hast commanded by thy servants the prophets, saying, The land, unto which ye go to possess it, is an unclean land with the filthiness of the people of the lands, with their abominations, which have filled it from one end to another with their uncleanness. 12Now therefore give not your daughters unto their sons, neither take their daughters unto your sons, nor seek their peace or their wealth for ever: that ye may be strong, and eat the good of the land, and leave it for an inheritance to your children for ever. 13And after all that is come upon us for our evil deeds, and for our great trespass, seeing that thou our God hast punished us less than our iniquities deserve, and hast given us such deliverance as this; 14Should we again break thy commandments, and join in affinity with the people of these abominations? wouldest not thou be angry with us till thou hadst consumed us, so that there should be no remnant nor escaping? 15O Lord God of Israel, thou art righteous: for we remain yet escaped, as it is this day: behold, we are before thee in our trespasses: for we cannot stand before thee because of this. (Ezra 9:1‑15); Ezra 10:11Now when Ezra had prayed, and when he had confessed, weeping and casting himself down before the house of God, there assembled unto him out of Israel a very great congregation of men and women and children: for the people wept very sore. (Ezra 10:1); Neh. 1:66Let thine ear now be attentive, and thine eyes open, that thou mayest hear the prayer of thy servant, which I pray before thee now, day and night, for the children of Israel thy servants, and confess the sins of the children of Israel, which we have sinned against thee: both I and my father's house have sinned. (Nehemiah 1:6); Neh. 9:2-32And the seed of Israel separated themselves from all strangers, and stood and confessed their sins, and the iniquities of their fathers. 3And they stood up in their place, and read in the book of the law of the Lord their God one fourth part of the day; and another fourth part they confessed, and worshipped the Lord their God. (Nehemiah 9:2‑3); Dan. 9:4-204And I prayed unto the Lord my God, and made my confession, and said, O Lord, the great and dreadful God, keeping the covenant and mercy to them that love him, and to them that keep his commandments; 5We have sinned, and have committed iniquity, and have done wickedly, and have rebelled, even by departing from thy precepts and from thy judgments: 6Neither have we hearkened unto thy servants the prophets, which spake in thy name to our kings, our princes, and our fathers, and to all the people of the land. 7O Lord, righteousness belongeth unto thee, but unto us confusion of faces, as at this day; to the men of Judah, and to the inhabitants of Jerusalem, and unto all Israel, that are near, and that are far off, through all the countries whither thou hast driven them, because of their trespass that they have trespassed against thee. 8O Lord, to us belongeth confusion of face, to our kings, to our princes, and to our fathers, because we have sinned against thee. 9To the Lord our God belong mercies and forgivenesses, though we have rebelled against him; 10Neither have we obeyed the voice of the Lord our God, to walk in his laws, which he set before us by his servants the prophets. 11Yea, all Israel have transgressed thy law, even by departing, that they might not obey thy voice; therefore the curse is poured upon us, and the oath that is written in the law of Moses the servant of God, because we have sinned against him. 12And he hath confirmed his words, which he spake against us, and against our judges that judged us, by bringing upon us a great evil: for under the whole heaven hath not been done as hath been done upon Jerusalem. 13As it is written in the law of Moses, all this evil is come upon us: yet made we not our prayer before the Lord our God, that we might turn from our iniquities, and understand thy truth. 14Therefore hath the Lord watched upon the evil, and brought it upon us: for the Lord our God is righteous in all his works which he doeth: for we obeyed not his voice. 15And now, O Lord our God, that hast brought thy people forth out of the land of Egypt with a mighty hand, and hast gotten thee renown, as at this day; we have sinned, we have done wickedly. 16O Lord, according to all thy righteousness, I beseech thee, let thine anger and thy fury be turned away from thy city Jerusalem, thy holy mountain: because for our sins, and for the iniquities of our fathers, Jerusalem and thy people are become a reproach to all that are about us. 17Now therefore, O our God, hear the prayer of thy servant, and his supplications, and cause thy face to shine upon thy sanctuary that is desolate, for the Lord's sake. 18O my God, incline thine ear, and hear; open thine eyes, and behold our desolations, and the city which is called by thy name: for we do not present our supplications before thee for our righteousnesses, but for thy great mercies. 19O Lord, hear; O Lord, forgive; O Lord, hearken and do; defer not, for thine own sake, O my God: for thy city and thy people are called by thy name. 20And whiles I was speaking, and praying, and confessing my sin and the sin of my people Israel, and presenting my supplication before the Lord my God for the holy mountain of my God; (Daniel 9:4‑20)). When John the Baptist was fulfilling his mission, the people “confessed” their sins, and were baptized (Matt. 3:5-65Then went out to him Jerusalem, and all Judea, and all the region round about Jordan, 6And were baptized of him in Jordan, confessing their sins. (Matthew 3:5‑6)); and of the Christian it is said, “If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness” (1 John 1:99If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness. (1 John 1:9): Compare Psalm 32:55I acknowledged my sin unto thee, and mine iniquity have I not hid. I said, I will confess my transgressions unto the Lord; and thou forgavest the iniquity of my sin. Selah. (Psalm 32:5)). We are exhorted to confess our faults one to another (James 5:1616Confess your faults one to another, and pray one for another, that ye may be healed. The effectual fervent prayer of a righteous man availeth much. (James 5:16)).
The other application of the term is confessing the Lord Jesus. The Jewish rulers agreed that if any one “confessed” that Jesus was the Christ he should be excommunicated (John 9:2222These words spake his parents, because they feared the Jews: for the Jews had agreed already, that if any man did confess that he was Christ, he should be put out of the synagogue. (John 9:22)). On the other hand, “If thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved..... Confession is made unto salvation.” This is PROFESSION, as indeed the same word, ὁμολογέω, is translated. “Let us hold fast our profession”—“profession of our faith” (Heb. 4:1414Seeing then that we have a great high priest, that is passed into the heavens, Jesus the Son of God, let us hold fast our profession. (Hebrews 4:14); Heb. 10:2323Let us hold fast the profession of our faith without wavering; (for he is faithful that promised;) (Hebrews 10:23)).

From Anstey’s Doctrinal Definitions:

Many evangelical Christians think that in order for a person to be truly saved, he must make a public confession of his faith in Christ. Romans 10:99That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved. (Romans 10:9) is used to support this idea. It says, “If thou shalt confess with thy mouth the Lord Jesus [Jesus as Lord], and shalt believe in thine heart that God hath raised Him from the dead, thou shalt be saved.” As a result, evangelical preachers often urge public confessions at their meetings and gospel rallies. They issue an "altar call" to their audiences, calling those who want to be saved to come forward and make a public declaration of their faith. However, if we make the confession of a person’s faith in Christ before men a condition of his eternal salvation, then the blessing of the gospel is not solely on the principle of faith. It becomes something that is based on faith and works! And this is contrary to the fundamentals of the Gospel (Rom. 3:26-31; 4:4-526To declare, I say, at this time his righteousness: that he might be just, and the justifier of him which believeth in Jesus. 27Where is boasting then? It is excluded. By what law? of works? Nay: but by the law of faith. 28Therefore we conclude that a man is justified by faith without the deeds of the law. 29Is he the God of the Jews only? is he not also of the Gentiles? Yes, of the Gentiles also: 30Seeing it is one God, which shall justify the circumcision by faith, and uncircumcision through faith. 31Do we then make void the law through faith? God forbid: yea, we establish the law. (Romans 3:26‑31)
4Now to him that worketh is the reward not reckoned of grace, but of debt. 5But to him that worketh not, but believeth on him that justifieth the ungodly, his faith is counted for righteousness. (Romans 4:4‑5)
; Eph. 2:8-98For by grace are ye saved through faith; and that not of yourselves: it is the gift of God: 9Not of works, lest any man should boast. (Ephesians 2:8‑9)). Moreover, it would mean that a person couldn't get saved if he were alone somewhere—because he has no one to make his confession to! According to this idea, he may have repentance towards God, and faith towards our Lord Jesus Christ” (Acts 20:2121Testifying both to the Jews, and also to the Greeks, repentance toward God, and faith toward our Lord Jesus Christ. (Acts 20:21)), but it wouldn’t be enough! There is an added condition—he must confess his faith to someone. But what if he were to die before he had a chance to tell someone of his faith in Christ? According to this teaching, he would be lost! Needless to say, this mistaken idea is not according to Scripture.
"Confess" in Romans 10:99That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved. (Romans 10:9) means "assent" (Strong's Concordance) or "to express agreement." The question is, to express agreement with whom? A. Roach said that in the light of Philippians 2:1111And that every tongue should confess that Jesus Christ is Lord, to the glory of God the Father. (Philippians 2:11) which says, "Every tongue should confess that Jesus Christ is Lord, to the glory of God the Father" and Romans 14:1111For it is written, As I live, saith the Lord, every knee shall bow to me, and every tongue shall confess to God. (Romans 14:11) which says, "Every tongue shall confess to God," it is clear that this confession is to be made to God, not to men. The believer acknowledges to God that “Jesus Christ is Lord.” H. A. Ironside said, "The confession here is not, of course, necessarily the same thing as where our Lord says, 'Whosoever shall confess Me before men, him will I confess before My Father which is in heaven.' This is rather the soul's confession to God Himself that he takes Jesus as Lord" (Lectures on Romans, pp. 130-131).
Paul mentions the "mouth" before the "heart" (which is the order found in Deuteronomy 30:1414But the word is very nigh unto thee, in thy mouth, and in thy heart, that thou mayest do it. (Deuteronomy 30:14)), but in Romans 10:1010For with the heart man believeth unto righteousness; and with the mouth confession is made unto salvation. (Romans 10:10), he reverses them, giving the actual order in which they occur when a person gets saved. Thus, an inward reception of the Word by faith results in an outward expression of one’s faith in a confession that “Jesus Christ is Lord.”
In normal conditions, a true believer will make a confession of his faith in Christ before his fellow men. This should happen quite naturally, for the good news of salvation is too good to keep to ourselves. Confession of our faith before men is good, and if a believer will not confess Christ before men, he will be denied a reward and an honourable mention before the Father in the coming day (Matt. 10:32-3332Whosoever therefore shall confess me before men, him will I confess also before my Father which is in heaven. 33But whosoever shall deny me before men, him will I also deny before my Father which is in heaven. (Matthew 10:32‑33))—but it is not a condition whereupon he is saved eternally. A new believer may be hesitant to confess Christ at first, but his eternal welfare does not depend upon it. Paul taught that the blessing of salvation is solely on "the principle of faith" (Rom. 1:17; 3:30; 4:16; 5:117For therein is the righteousness of God revealed from faith to faith: as it is written, The just shall live by faith. (Romans 1:17)
30Seeing it is one God, which shall justify the circumcision by faith, and uncircumcision through faith. (Romans 3:30)
16Therefore it is of faith, that it might be by grace; to the end the promise might be sure to all the seed; not to that only which is of the law, but to that also which is of the faith of Abraham; who is the father of us all, (Romans 4:16)
1Therefore being justified by faith, we have peace with God through our Lord Jesus Christ: (Romans 5:1)
). He would be contradicting himself here in Romans 10:99That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved. (Romans 10:9), if he were to put the condition of confession before men on a person’s salvation.
The second kind of confession has to do with sins, but it is in connection with a believer being restored to communion with God. 1 John 1:99If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness. (1 John 1:9) says, "If we confess our sins, He is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness." The “we” in this verse refers to children in the family of God—the Christian company. A believer who has failed, having allowed sin in his life, needs to retrace his course in repentance to the starting point of his departure from the Lord and confess those sins to God the Father. By doing this, he judges himself and gets to the bottom of the cause for his departure. Someone asked J. N. Darby about a situation where one has in a general way drifted away, but he cannot think of any particular sin that has been the cause of it. He said that if that were the case, the person can confess that his state was bad.
Many have the idea that repentant sinners who come to Christ for salvation must confess their sins. But Scripture does not say this. If it were necessary to do this to get saved, then no one would be saved! What sinner can remember all of his sins? Especially when we take into consideration that "the plowing [thoughts] of the wicked is sin" (Prov. 21:44An high look, and a proud heart, and the plowing of the wicked, is sin. (Proverbs 21:4)) and "the thought of foolishness is sin!" (Prov. 24:99The thought of foolishness is sin: and the scorner is an abomination to men. (Proverbs 24:9)) This being the case, our sins must number in the thousands—maybe in the millions! It would be an impossible task for a sinner to confess all that. Thankfully, God does not put this condition on the salvation of our souls. The sinner seeking salvation is to own (or confess) that he is a sinner, and in believing, he is to confess Jesus as Lord. But God does not require that he must confess each and every sin that he has committed in his life in order to be saved.