Coaster brake hubs apply the brake when you turn the pedals backwards. Most children's bikes in the U.S. come with coaster brakes, but they are not all that practical.
Coaster brakes make it difficult to start up, because they don't permit you to rotate the pedals backward to get into a good starting position.
Coaster brakes are generally quite reliable, but when they fail they tend to fail suddenly and completely. As a result we do not recommend relying on a coaster brake alone for braking--you should also have a hand brake, preferably working on the front wheel, so there will be a backup system in case the chain breaks or derails. Shimano is the best currently available.