Your belly is your stomach. If you have a belly ache, you have a pain in your abdomen.
Santa Claus is famous for his jolly laugh and his large belly. The word belly is a more casual way to say "stomach" or "abdomen," just as your navel is informally called a "belly button." A less common way to use the word is as a verb meaning "to swell," which is actually the oldest meaning of belly, from the Old English belig, "bag," and a Germanic root meaning "to swell like a bag."