Repentance means first of all, to acknowledge our sins, to be truly sorry for them. This “godly sorrow” comes from the Holy Spirit convicting us with God’s law.
But the Bible also uses the work of repentance in a broader sense to include faith in Jesus our Savior. This faith is produced by the Holy Spirit, who convinces us through the Gospel that our sins are forgiven for the sake of Jesus, who lived, died and rose again for us.
Put those two concepts together and you have repentance in its fullest sense. (Jesus told His disciples in Luke 24:47 that repentance and forgiveness of sins will be preached in His name to all nations.)
According to the Bible, those who are truly sorry for their sins and trust in Jesus as their Savior also want to turn away from their sins, intending with the help of the Holy Spirit not to keep on living a life of sin.
If we want to keep on sinning, we need to ask ourselves if we have really repented. However, we are weak human beings and although we do not want to commit the same sins again and again, we may sometimes fall into sin out of weakness.
Whenever we sin, we know (as John says) that “if we confess our sins, [God] is faithful and just and will forgive our sins” for the sake of Jesus our Savior (1 John 1:9). If repentance becomes a “game” with God and we don’t really want or intend to stop committing a certain sin (say stealing), and we go on stealing, living always in that sin of stealing, then we place ourselves in grave spiritual danger. We need to ask that God the Holy Spirit to give us the power to stop committing that sin and trust Him to help us fight against it.
Sad to say, the desire to sin may come back at times, for which we will have to repent again. That’s not the same as living in sin. We all commit all kinds of sins daily, for which we have to daily repent. As long as we are sorry for our sins and believe that God forgives our sins for Christ’s sake, we will be forgiven and have eternal life.
Worldly sorrow is the kind of sorrow Judas Iscariot had, which caused him to commit suicide. It was a self-centered remorse and despair that wrongly concluded that all was lost in this life, that there was no hope, that there was nothing God could do. 2 Corinthians 7:10 says that this kind of sorrow brings death. But godly sorrow is true sorrow over sin accompanied by trust in Jesus for forgiveness. This is the kind of sorrow Peter had after he denied Jesus, and King David had after he committed adultery and murder (Psalm 51). Godly sorrow leads to life and salvation, because it includes faith in Jesus Christ.