If you're unrepentant about something, you refuse to regret it or apologize for it. An unrepentant cheater might brazenly lean over to get a better look at his friend's chemistry test.
If you're repentant about something you've done or said, you feel terrible about it, and you express shame and remorse. If, on the other hand, you're unrepentant, you're not at all sorry. An unrepentant gossip doesn't feel guilty about spreading rumors. The word comes from the Vulgar Latin penitire, "to regret."