The running walk is a unique gait natural to some breeds of horses, most notably the Tennessee Walking Horse. It's basically a fast walk, somewhat like those crazy mall walkers you see. A normal horse walks at around 4-5 miles an hour, a walking horse can do a running walk at about 10-15 miles an hour, about what a trot would be. The huge advantage of this is that the running walk is an extremely smooth gait, unlike a trot. It's also very efficient, so the horse can cover large distances of ground with little effort.