I have a gap near the side of my mouth and the dentist mentioned the option of a bridge. What is a bridge?

A classical dental bridge (now called a "fixed partial denture") is like two crowns, with a false tooth between them. The whole bridge is cemented in place, thus the missing tooth is replaced by the replica tooth between the two crowns. Bridges can be much more complicated than this and different types exist. 

Sometimes, the bridge is glued to the backs of the teeth each side of the space, instead of putting a crown over the whole tooth. This is known as a 'Maryland Bridge'.