The popular but deeply flawed view of repentance is one of an unpleasant practice that torments the religious while they continuously struggle against doing what they know they shouldn't.
Repentance is the act of abandoning flawed actions, desires, or thoughts in preference for something better. In short, repentance is improvement.
All people have the capacity to conceive of improvement. You need not believe in God to practice or benefit from repentance. It will lead all people closer to what they desire, no matter what they desire. However, all repentance will eventually lead to God, and God will lead a person to all repentance, as he is both the source and destination of all improvement.