"butt" is short form for the word "buttock or buttocks".
A buttock (singular) is the fleshy part that we sit on.
Buttocks would then mean both round fleshy parts that forms our "back end, backside, behind, bottom, bum, butt, derriere, fanny, gluteus maximus, haunches, hindquarters, posterior, rear, rump, seat, cheeks, and ass".
So, "Sit your butt down" means "sit down", however, it is a disrespectful expression, usually said in anger, and should never be used in formal situations.