The adjective remorseful is good for describing someone who is really, really sorry — like a teenager who borrows his parents' car without asking and drives it into a tree.
Someone who feels remorseful has usually done something that he or she now feels guilty about. A defendant at a murder trial might be remorseful, and so might a little girl who has accidentally stepped on her cat's tail. The word remorseful means "full of remorse," and remorse comes from the Latin word remordere, "vex," or literally "to bite back." A popular phrase in Medieval Latin was remorsus conscientiæ, or "a biting back of one's conscience."