The following question and answer are from the GotQuestions.org website. I thought it would be interesting to record these here plus my comment on the Got Questions blog. Since I preach the need people have to "repent and believe," I am always interested in these kinds of discussions!
Question: "What is repentance and is it necessary for salvation?"
Answer: Many understand the term repentance to mean “turning from sin.” This is not the biblical definition of repentance. In the Bible, the word repent means “to change one’s mind.” The Bible also tells us that true repentance will result in a change of actions (Luke 3:8-14; Acts 3:19). Acts 26:20 declares, “I preached that they should repent and turn to God and prove their repentance by their deeds.” The full biblical definition of repentance is a change of mind that results in a change of action.
What, then, is the connection between repentance and salvation? The Book of Acts seems to especially focus on repentance in regards to salvation (Acts 2:38; 3:19; 11:18; 17:30; 20:21; 26:20). To repent, in relation to salvation, is to change your mind in regard to Jesus Christ. In Peter’s sermon on the day of Pentecost (Acts chapter 2), he concludes with a call for the people to repent (Acts 2:38). Repent from what? Peter is calling the people who rejected Jesus (Acts 2:36) to change their minds about Him, to recognize that He is indeed “Lord and Christ” (Acts 2:36). Peter is calling the people to change their minds from rejection of Christ as the Messiah to faith in Him as both Messiah and Savior.
Repentance and faith can be understood as “two sides of the same coin.” It is impossible to place your faith in Jesus Christ as the Savior without first changing your mind about who He is and what He has done. Whether it is repentance from willful rejection or repentance from ignorance or disinterest, it is a change of mind. Biblical repentance, in relation to salvation, is changing your mind from rejection of Christ to faith in Christ.
It is crucially important that we understand repentance is not a work we do to earn salvation. No one can repent and come to God unless God pulls that person to Himself (John 6:44). Acts 5:31 and 11:18 indicate that repentance is something God gives—it is only possible because of His grace. No one can repent unless God grants repentance. All of salvation, including repentance and faith, is a result of God drawing us, opening our eyes, and changing our hearts. God's longsuffering leads us to repentance (2 Peter 3:9), as does His kindness (Romans 2:4).
While repentance is not a work that earns salvation, repentance unto salvation does result in works. It is impossible to truly and fully change your mind without that causing a change in action. In the Bible, repentance results in a change in behavior. That is why John the Baptist called people to “produce fruit in keeping with repentance” (Matthew 3:8). A person who has truly repented from rejection of Christ to faith in Christ will give evidence of a changed life (2 Corinthians 5:17; Galatians 5:19-23; James 2:14-26). Repentance, properly defined, is necessary for salvation. Biblical repentance is changing your mind about Jesus Christ and turning to God in faith for salvation (Acts 3:19). Turning from sin is not the definition of repentance, but it is one of the results of genuine, faith-based repentance towards the Lord Jesus Christ.
My Comment: I too like your explanation of repentance, but I do see our need to repent having to do with changing one's mind in regard to his or her sin in some of the contexts that you brought up. For example, you mention John the Baptist's emphasis on producing "fruit in keeping with repentance" to support, rightfully, your claim that a change of mind regarding Christ will result in a change of behavior. But was John the Baptist calling people to a change of mind regarding Christ there? Christ hadn't even appeared on the scene yet. Based on the context, it is clear that the Baptist was calling his hearers to a "change of mind" regarding their sin. Two verses earlier Matthew tells us: "Confessing their sins, they were baptized by him in the Jordan River." Let's see if we can find "sin" in the context of other "repentance" verses and passages: Luke 5:32 says, "I have not come to call the righteous, but sinners to repentance." Luke 15:7 says, "I tell you that in the same way there will be more rejoicing in heaven over one sinner who repents than over ninety-nine righteous persons who do not need to repent." Luke 17:3 says, "So watch yourselves. "If your brother sins, rebuke him, and if he repents, forgive him." Luke 24:47 says, "and repentance and forgiveness of sins will be preached in his name to all nations, beginning at Jerusalem." The clincher: "I am afraid that when I come again my God will humble me before you, and I will be grieved over many who have sinned earlier and have not repented of the impurity, sexual sin and debauchery in which they have indulged" (2 Cor. 12:21). I did like your emphasis on repentance being as much a gift as faith is. And you "redeemed yourself" at the end by stating: "Turning from sin is not the definition of repentance, but it is one of the results of genuine, faith-based repentance towards the Lord Jesus Christ." Thanks.