What is the importance of cheeks, and how do we know if a dinosaur had them?

A hadrosaur skull. Compared with the surrounding bone, the parts of the jaw where the teeth grew are set in toward the center of the skull.  This creates the same kind of gap you feel on your face if you press against your cheek bones and lower jaw, then slide your fingers inward to feel your teeth.

The teeth of this hadrosaur are set inward from the side of the skull. Click to zoom.

Most reptiles do not have cheeks, and this limits how much food they can chew before swallowing. Without cheeks, food tends to fall off the teeth and out of the mouth - very counterproductive! Cheeks help animals to keep food in place while they chew it. Because well-chewed food is easier to digest it supplies more nutrients. Cheeks are made of soft flesh, which typically doesn't fossilize, but scientists believe that indirect evidence of cheeks can be found in the shape and arrangement of the skull and jaw in many plant-eating dinosaurs. You can see that the teeth of this hadrosaur, for example, are set in from the side of the skull and jaw, creating a gap that might have been covered by cheeks.