Riding, whether it's jumping, racing, or just pleasure riding, requires control of the horse.
Dressage, where the rider displays skill at controlling the horse, is the basis for all other forms of riding.
But dressage is basic not just basic riding skill. It gets quite competitive, and can be very challenging. It takes years to teach a top dressage horse to compete at high levels.
The skills displayed in the arena are called menage patterns.
Here are some of these patterns or "moves":