Sacrifice

Boyd’s Bible Dictionary:

(making sacred). Propitiatory, atoning or thanksgiving offering to God. An ordained rite (Lev. 17:4-9; Deut. 16:5-19). Sacrificial offerings numerous; but chiefly, the “burnt-offering” (Lev. 1:1-17); “sin-offering,” and “trespass-offering” (Lev. 7:1-10); “peace-offering” (Lev. 7:11-34); the latter also a “free-will” offering. These offerings could not satisfy God’s holy requirements for removing sin, but they were required of all under the law, until Christ’s sacrifice of Himself, which can and did once and for all put away sin for the believer (Heb. 9-10).

Concise Bible Dictionary:

As a technical religious term “sacrifice” designates anything which, having been devoted to a holy purpose, cannot be called back. In the generality of sacrifices offered to God under the law the consciousness is supposed in the offerer that death, as God’s judgment, was on him; hence the sacrifice had to be killed that it might be accepted of God at his hand. In fact the word sacrifice often refers to the act of killing.
The first sacrifice we read of was that offered by Abel, though there is an indication of the death of victims in the fact that Adam and Eve were clothed by God with coats of skins. Doubtless in some way God had instructed man that, the penalty of the fall and of his own sin being that his life was forfeited, he could only appropriately approach God by the death of a substitute not chargeable with his offense; for it was by faith that Abel offered unto God a more excellent sacrifice than Cain (Heb. 11:4). God afterward instructed Cain that if he did not well, sin, or a sin offering, lay at the door.
The subject was more fully explained under the law: “The life of the flesh is in the blood: and I have given it to you upon the altar to make an atonement for your souls: for it is the blood that maketh an atonement for the soul” (Lev. 17:11). Not that the blood of bulls and of goats had any inherent efficacy to take away sins; but it was typical of the blood of Christ which is the witness that they have been taken away for the believer by Christ’s sacrifice.
Christ appeared once in the end of the world “to put away sin by the sacrifice of himself;” and He having once died, there remains no more sacrifice for sins (Eph. 5:2; Heb. 9:26; Heb. 10:4,12,26). Without faith in the sacrificial death of Christ there is no salvation, as is taught in Romans 3:25; Romans 4:24-25 and 1 Corinthians 15:1-4.
The Christian is exhorted to present his body a living sacrifice, holy, acceptable unto God, which is his intelligent service (Rom. 12:1; compare 2 Cor. 8:5; Phil. 4:18). He offers by Christ the sacrifice of praise to God, and even to do good and to communicate are sacrifices well pleasing to God (Heb. 13:15-16; compare 1 Pet. 2:5). For the sacrifices under the law see OFFERINGS.