Your butt is your buttocks, your tush, your rear end. Saying butt is more childish than offensive.
Butt is a four-letter word, though using it won't get you in much trouble — It's much less offensive than ass. It also has plenty of other meanings, like butting into a conversation (interrupting it) or the butt of a gun (the thick end). If you make fun of someone, they are the butt of your jokes. The used end of a cigarette is called a butt, too. But you'll hear it more often in phrases like "Get your butt in here!"