The goal of the Art of Riding is to develop the horse from its natural balance to a riding balance. This is important to carry the rider properly. Piaffe contributes to realize this goal.
riding balance: weight on the hindquarter natural balance: weight on the front
Piaffe-work helps to move the weight to the hind legs and develops carrying capacity in the horse. This reduces the weight on the shoulders making them freer.
Also, the exercise is gymnastics for the horse and helps build up muscles of the entire upper-line.