"Jesus...is the one whom God exalted to His right hand as a prince and a savior, to grant repentance to Israel, and forgiveness of sins." Peter, Acts 5:30-31.
The Bible teaches that repentance is a gift from God.
In this passage, Peter states to the Sanhedrin that God placed Jesus at His right hand in order to grant repentance to Israel. In other words, Jesus does not only grant the blessing of repentance (God's forgiveness) but the change of heart which secures the blessing.
This truth is supported elsewhere in Scripture. In Acts 11:18, the Jerusalem elders realized from Cornelius' conversion that God had granted repentance to Gentiles. God didn't just granting eternal life to Cornelius, but the repentance that leads to life. Hebrews 6:6 says that spiritual renewal is unto repentance. Repentance doesn't cause inner renewal, but inner renewal causes repentance. In 2 Timothy 2:25, Paul counsels gentleness toward unbelievers, in case God grants them repentance.
The same truth is taught regarding faith, which is the conjoined-twin to repentance, Christ told a crowd that they could not believe in Him apart from divine drawing (John 6:44). He repeats this in 6:65, saying strongly that no one can believe in Him unless God grants it.
Jesus further said that God's gift of faith is always successful. Everyone to whom God gives the gift of faith comes to Christ (6:45), and as a result cannot be eternally lost (6:39-40). Paul says the same in Ephesians 2:8-9. Even though the pronoun "that" doesn't specifically refer to the word "faith" (since the word-gender of "faith" is feminine and "that" is neuter), it does refer to the entire preceding clause, "by grace you have been saved through faith". All of it -- grace, salvation, faith -- is a gift.
This is an important truth to know, because it keeps us from evangelistic self-reliance and manipulation, and it promotes evangelistic praise. It protects us from self-reliance, when we realize that we absolutely cannot force anyone to believe in Christ. We cannot using natural means force a true conversion, because there is something fundamentally, radically wrong with every person's soul, because of the enslaving power of sin and Satan.
We in our preaching and witnessing are dependent on God. We will also be more ethical, and avoid emotionally manipulating people into false conversions. We will not try to push their emotional red-buttons, or confuse their tears with new birth. We also give thanks, never to ourselves but only to God, for every person who truly comes to Christ. This truth also provokes prayer for non-Christians, since only individual divine intervention can bring a sinner to repentance.
Every lost person ought to repent, because it's God's will that they should. Sin is always wrong, and obedience is God s always right, regardless of how spiritually unwilling a lost person is. God will use the impenitent to glorify Himself on the day of their judgment (Proverbs 16:4). We preach to all, without discrimination, that each one should repent and turn to Christ. But God must give the gift of repentance, for their heart-attitudes toward sin and God to change.