To be impenitent is to have no remorse or regrets. Your brother was impenitent when he ate the cupcakes that you had baked for your club fundraiser. Not nice.
The word repent is hiding in impenitent. When you repent, you regret or feel sorry about something you've done. Impenitent and repent share the Latin root penitire meaning "to regret," but add im- meaning "not" for impenitent and you've got the opposite: "to not regret or repent." A criminal who is impenitent about feels no shame about what he's done.