Recommendation: Before this exercise practice another called "Three Step Stop." After this exercise practice "The Clock Work Exercise" (which teaches diagonals)
Before you begin Hip-Shoulder-Shoulder, you should have practiced "Three Step Stop." That exercise would have begun to teach your horse to not carry so much weight on the front half of his body. So instead of leaning or dropping the balance of his weight onto his shoulders, (when he stops for instance) he would have learned to stay more maneuverable by carrying more weight more evenly throughout his body with his back end doing more of it's fair share. He'll begin traveling with his shoulders "raised" as opposed to "dropped." (You experienced a dropped shoulder the last time your leaned into a turn and you felt like sliding off. You probably blamed the fit of the saddle or figured your cinch was too loose.)
We'll continue to build on that previous exercise by teaching the horse to disengage his hindquarters in this one. "Disengaging" is a fancy way of saying "The front end stops; the back end moves around like the hands of a clock." Think of a turn on the forehand or a one-legged duck swimming in circles.
Practice Hip-Shoulder-Shoulder to gain more control over your horse's shoulders (so your knee won't hit that tree, so he won't "dive into his turns," etc.), to teach your horse to back with far less resistance - and to take a giant step toward teaching your horse to carry itself in a more collected fashion. ("Collection" equates to turning without leaning, turning now instead of later, etc.)
But this exercise, Hip-Shoulder-Shoulder, has become a "classic" exercise for one very big reason: It gives you control of your horse's stop. Every horse-related problem you can think of comes down to "going and stopping." "I can't get my horse to cross the creek." "I can't get my horse to go in the arena." "I can't get my horse to go away from another horse." And people get hurt when they can't stop their horse: "I can't get my horse to stop bucking, stop rearing, or stop kicking." We spend most of our training time, (as in this exercise) dealing with, and practicing, "going and stopping" because that's where you need the most control.
If you pick up two reins to stop your horse, he might stop - but without the correct training he's