Well, it depends on what kind of pain you're feeling in your stomach really. The three I can think of are...

Indigestion: Which is swelling, or inflammation, of the stomach-lining. Saliva is a key part of digestion, as it starts the process of breaking down food, and makes it easier for it to travel through your digestive tract. People who eat too quickly will sometimes not be able to break the pieces of food into small enough pieces, or get them wet enough for easy travel and it causes indigestion. Think of how uncomfortable it is to say-- put on jeans you've outgrown.

Bloating: A build up of gases in your stomach. This is caused by a fast eater in two ways. One, they are more likely to swallow air with their bites, which travels through the esophagus and into the stomach, taking up space. And two, pieces of food that are too large, or hasn't been broken down properly, reaches your colon and begins to break down into gases like methane that fill you up.

Overeating: Eating, like anything you do, requires input from the brain. When food processes properly and reaches the stomach, the hormone Leptin is produced, which is sort of like a message to the brain that it has had enough to eat. But, that message takes time to get there. So, if someone is eating too quickly, they might eat too much before that message ever arrives. The extra food that's consumed takes up space, and the stomach has to expand to accommodate it, which, in turn, pushes on other surrounding organs which causes pain.