What is repentence? Repentence is asking to be forgiven of your sins; it's coming to terms with them and true repentence resutls in NEVER going back to that sin. People would often ask for forgiveness, and are forgivene, but then would fall again. That doesn't happen with true repentence, which results in newness of life (Acts 11:18). It's the goodness of God that leads us to that repentence (Romans 2:4), since He is just a God of love & mercy.
Though repentence is a New Testament doctrine, the best Old Testament expample us Psalm 51, where David repents for his ilicit relation with Bathsheba, the wife of Uriah the Hittite, one of his best generals, Those events can be read in 2 Samual 11.