In the context of triathlon training, a brick is any training session that combines more than one of the three disciplines with minimal or no interruptions between. The most common brick is a bike/run combination because this transition is generally considered to be the most challenging.
The origin of the term is the strange, heavy feeling many experience in the legs when they switch from biking to running. (Personally, I would have named it Jell-o, but there are probably copyright problems with that.)
The purpose of a brick workout can vary. Obviously, it's a good preparation for the race and allows the athlete to simulate race conditions. Bricks can also be used for overall aerobic endurance or to prepare for certain aspects of the race. For example, a brick with the emphasis on a long bike ride would help prepare the athlete to pace a ride appropriately so as to be able to still run afterwards.