Brick is a mild tasting cheese which originated in the U.S. in the late 1800's. Legend has it that John Jossi, a Swiss immigrant living in Wisconsin, came up with the first brick cheese by pressing Limburger curd between two bricks. Brick is a very common cheese in Wisconsin, although it becomes more difficult to find the further you roam from America's Dairyland.
Alternately classified as a semi-soft or firm cheese, brick is slightly softer than cheddar, but more firm than a brie. The nutty, yet sweet, flavor which is characteristic of brick cheese can develop to a pungency rivaling its parent Limburger as it ages. Because of this, the ripening and aging environments must be carefully controlled to prevent unwanted flavors.
The comparatively lower fat content of brick makes it a very good melting cheese, as it does not become overly greasy. It is also excellent for eating sliced either on sandwiches, by itself, or with fruit and bread. Food and wine which compliment brick cheese depend on whether you are eating the "young" or "aged" version. Strong flavors will overpower "young" brick, but suit "aged" brick perfectly, so make sure you know which type you are getting.
Sources and trivia:
Some very interesting person devoted this lime green website to the glories of brick cheese. Wear sunglasses.
And for the truly cheese-obsessed, may I recommend CheeseNet?