Beer has a lot of calories. Drinking a lot of beer makes you fat. People call a large stomach that comes from drinking too much beer a "beer belly".
When I think of a "beer belly", I usually think of a person who isn't too fat, but whose stomach sticks out a lot. This is also called a "pot belly" because it's shaped a little bit like a pot that's sticking out of your stomach.
People usually think of a "beer belly" as being something that a man has. If you say that a woman has a beer belly, it sounds funny. Sometimes a woman will say that she has a beer belly as a joke, though.
When you say that someone has a "beer belly", it doesn't sound that negative. It kind of sounds cute, actually.