It sounds like pork belly is the belly of a pig, but that is not the case. It is actually the part that runs on the underside of the hog and surrounds its stomach. It is a really long piece of meat that has quite a bit of fat in it, which makes it great for making bacon or pancetta.
Sometimes you may see this on menus at restaurants being made fresh. It is usually called braised pork belly, and it is rather good. You can do the same at home, either braise the pork belly or make it into bacon.