Onomatopoeia is how Thwomp gets his name. You see, Thwomp thwomps, and he loves his job. He hangs out on the ceiling of Bowser’s fortresses and waits to crush you. There are two ways to kill a Thwomp, hammers and statue drops (just like with Roto-Disc). Some Thwomps move horizontally later in the game. They’re versatile like that.
[EDIT: Corrected spelling at Tom's suggestion.]