Beef cheeks are exactly what they sound like. They are the muscles in the facial cheeks of cattle. They are a finely textured meat with some internal silverskin.
Following the general rule that the more a muscle is used, the tougher it gets when cooked, beef cheeks are best marinaded overnight and then braised in a long, slow process. This technique produced the tenderest results. You can use your favorite recipe for braised beef ribs, classic French Boeuf en Daube, or even Osso Bucco recipe, although the last one may need to cook longer at a lower temperature. Personally, I would lean toward something that uses a full bodied red wine and a hearty beef stock.
If you can't find a beef cheeks, brisket or flank can be used instead, although the texture may be not quite as fine.