Let's start at the very beginning!

The competition can be likened to
Dressage with Obstacles. The obstacles being similar to Working Equitation and Trec competitions. Here it was being judged on style and skill as opposed to speed although there is a speed class as well. 

In this photo, the course was begun with your horse standing still, whilst you transfer the mug from one side to the other. Then preceding  to circle a small animal pen on both reins.