Concise Bible Dictionary:
This is from ἐπιστρέθω, “to turn to.” It is in scripture the real effect that accompanies the new birth, a turning to God. It is beautifully expressed in the case of the Thessalonians, showing how they “turned to [the same word] God from idols, to serve the living and true God” (1 Thess. 1:9). Paul and Barnabas were able to make known to the saints the “conversion of the Gentiles” (Acts 15:3). In Peter’s address to the Jews he said, “Repent ye therefore, and be converted, that your sins may be blotted out” (Acts 3:19). Without being converted they could not enter the kingdom of heaven (Matt. 18:3). The word is used in a somewhat different sense in respect to Peter himself. The Lord, knowing that he would fall under the sifting of Satan, said, “When thou art converted strengthen thy brethren”; that is, when he had returned in contrition, or been restored. In the Old Testament the Hebrew words signify the same, “to be turned,” “to turn back” (Psa. 51:13; Isa. 6:10; Isa. 60:5; compare Isa. 1:27, margin).
Strong’s Dictionary of Greek Words:
Transliteration:
epistrophe
Meaning:
from 1994; reversion, i.e. morally, revolution
From Anstey’s Doctrinal Definitions:
This refers to a person’s heart being turned toward God (Psa. 19:7; 51:13; Jer. 31:18; Ezek. 33:11; Luke 1:16). Initially, conversion occurs when a person is born of God (Matt. 18:3; Acts 3:19; 15:3; 26:18; 1 Thess. 1:9, etc.), but it is not used exclusively for a person’s new birth and salvation, as many think. If, at some time later in a believer’s life, he were to become careless in his walk and turn to the world, he would need to be converted again. Hence, it is possible for someone to be converted more than once—but it is a sad thing indeed if he should require subsequent conversions. This does not mean that if a believer fails, he loses his salvation and needs to get saved all over again, but rather, that he needs his heart turned back to the Lord for the restoration of his communion with God.
W. Kelly said, “Scripture uses it [conversion] not merely for the first turning to God, but for a turning again to Him if one has slipped away. This is really the main distinction between conversion and quickening. For quickening can only be once, but conversion may be repeated” (Lectures Introductory to the Study of the Minor Prophets, p. 378).
James said, "Brethren, if any of you do err from the truth, and one convert him; let him know that he which converteth a sinner from the error of his way shall save a soul from death, and shall hide a multitude of sins" (James 5:19-20). By saying, "Brethren, if any of you..." it is clear that James was referring to believers. Real believers can "err from the truth" and fail, and if they do, they need to be converted again. The "death" that James speaks of here is physical death, which God might allow in a wayward believer's life as a governmental judgment, if he does not repent (1 John 5:16; 1 Cor. 5:2; 11:30; Ex. 30:21; Eccl. 7:17). This doesn’t mean that a believer who dies under the hand of God’s governmental judgment loses his soul’s salvation, for God's governmental dealings with His people pertain only to their time on earth; it does not touch their eternal standing and destiny.
The Apostle Peter is an example of a believer having a second conversion. The Lord said to him, "Simon, Simon, behold, Satan hath desired to have you, that he may sift you as wheat: but I have prayed for thee, that thy faith fail not: and when thou art converted, strengthen thy brethren" (Luke 22:31-32). Peter had come to know the Lord earlier in the Lord's ministry and was converted at that time. But then, some 3½ years later, Peter denied Him, and consequently, he needed to be converted again (Mark 16:7; Luke 24:34; John 21:15-19). Note: the Lord did not pray that Peter's soul’s salvation and eternal security wouldn't “fail”—because it can’t fail—but that his faith would not fail when his heart turned away from the Lord.
James 5:19 and Luke 22:32 in the J. N. Darby translation renders “converted” (the KJV) as “restored” in order to help distinguish a person’s initial conversion from a subsequent conversion that he might have. But W. Kelly states that rendering those verses as “restored” is really a paraphrase because the literal meaning of the word is converted, which is to have the heart turned toward God (Lectures Introductory to the Study of the Minor Prophets, p. 378).