If you watch a horse race, you'll see that jockeys ride in a very different way from anyone else who mounts a horse.
They balance on the stirrups, crouched above the horse's back. A lot of people think this is to reduce drag - however, a crouched jockey is not actually any lower than a person sitting on a horse normally. The answer is more biomechanical.
The modern jockey seat was invented in America in the late nineteenth century. It was created by trial and error - jockeys discovered that it gave their horses a 5% speed boost. Of course, once a few jockeys started doing it, they all had to.
The trick is that they zig when the horse zags. When the horse's back comes up, the jockey crouches lower, when the horse's back drops, he rises a little more. This is much harder work for the jockey - but it means that the horse is not lifting the jockey up and down - the jockey is. The horse's back moves up and down 6 inches, the jockey only moves 2.