"To have the horse trot around beside you in a circle, staying exactly 4 feet away while remaining relaxed, maintaining an arc in his body and keeping slack in the lead rope both in the circle and during changes of direction."
This exercise teaches the horse to bend more in the ribs and softer in the halter. They're also a lot closer to you (4 feet) than they are in lunging. But this exercise is really good for a nervous, reactive horse as well as a pushy horse.
Pushy horses: Been able to work beside you but respect your space. This also helps have them pay attention to you while working so close to you on the ground.
Softer: Arcing that rib cage and getting softer will also help for when you're in the saddle. Softer circles!
Lighter in the halter: This helps for when you pull on the halter for the horse not to pull against it but go with your direction.