What is true repentance? Is it saying you're sorry? Is it confessing sin to God? Or is it more than that?
A friend of mine and I were discussing repentance one time, and he commented that the problem with genuineness of repentance is that the individual receives the benefit of his or her sin. For instance, a high schooler who lies to his parents and gets caught still got to go see the movie. Is the remorse a result of being caught or a result of a changed spirit?
David did not get receive the benefit of his sin. If it wasn't enough to have the death of one person on his shoulders, he had to deal with the death of an infant. And when, through Nathan, David found out that God was going to take the baby's life, he pleaded with God to change His mind. David's emotion was such that his servants were afraid to tell him when the baby died for fear that he would take his own life. I believe David was truly sorry not necessarily because he did all of that but because we know that he never committed his sin again.
The nature of true repentance is both sorrow and reform. One can't truly be repentant and still go on living in the same manner. In God's Pursuit of Man, AW Tozer wrote the following about repentance:
The truest and most acceptable repentance is to reverse the acts and attitudes of which we repent. A thousand years of remorse over a wrong act would not please God as much as a change of conduct and a reformed life.
Change of conduct. A reformed life. Those are the nature of true repentance.