Disengagement of the hindquarters occurs when your horse crosses his hind legs. Your horse’s “motor” is in his hind end. So, when his hind legs cross, the engine is in neutral; your horse stops forward impulsion. Disengagement also encourages your horse to have a submissive attitude. You’re taking away his flight response. Disengagement is a natural, voluntary behavior for horses and it signals contrition. In natural settings, it’s only seen in neonatal foals.
Use disengagement as a tool to refocus your horse and stop his forward impulsion. You should be able to disengage your horse from the ground and from the saddle—both are easy to do. Simply drive your horse forward then tip his nose up and to the inside as he steps up under himself with his inside hind leg.
The one-rein stop is an example of how you might disengage a horse from the saddle. Horses actually stop better off one rein than two, because when you pull on two reins to stop, the horse braces his neck, leans into the bit and may even run through the bridle. He can’t lean on one rein, and he can’t lean when his neck is bent.
By lifting one rein, toward your belly button or opposite shoulder, you lift your horse’s nose and shoulder as he crosses his hind legs. You’ll know when your horse disengages because you’ll feel his legs cross—his back will feel very crooked underneath you. As soon as your horse begins to disengage—or even slow down—release the rein to reward his response. You should be using less of a rein aid every time you ask for the one-rein stop. Try to alternate between using the right and left rein, so your horse is working balanced on both sides of his body.
You can also require your horse to continue moving forward while he brings his inside hind leg underneath his belly—like when you leg-yield, two-track, side pass or turn on the forehand, from the ground or in the saddle. This is much more difficult for your horse than walking straight, so don’t ask too much of your horse and make him resent the movements.
My groundwork and riding videos—especially Lead Line Leadership and GPR Volume 5 Refinement and Collection—explain the specific aids required to cue your horse for disengagement and lateral movements and shows a series of progressive exercises to develop the horse and rider/handler.