Gullet is another name for the esophagus, the organ that food passes through on its way to the stomach. When you eat a cupcake, it moves from your mouth to your pharynx, and then to your gullet.
The gullet is an important part of your digestive system, linking your mouth and stomach, and also one of the earliest steps in the digestive process. Muscles in the gullet contract and relax, helping to push food along, a process that's called peristalsis. Gullet comes from the Old French golet, "neck of a bottle," from the Latin gula, "throat."