Well, because Im not very good at explaining things, I'm just going to copy and paste a thing from the site.
"Centered Riding® is an innovative way of expressing the classical principles of riding, using body awareness, centering, and imagery. Centered Riding® encompasses all seats and styles of riding. It teaches a language that allows clearer communication between horse, rider, and instructor. Centered Riding® was developed by Sally Swift, author of the best-selling book and videotapes, and is now taught by Centered Riding Instructors around the world.
Centered Riding® is based on a knowledge of human and horse anatomy, balance, movement, and on understanding how the mind affects the body and how both affect the horse. It uses centering and grounding techniques from the oriental martial arts, along with body awareness, mental imagery and sports psychology. Through increasing body awareness, inhibiting old patterns, and replacing them with a more balanced, free, and coordinated use of self, both horse and rider can move more freely and comfortably, and develop their best performance. "
Taken from: www.centeredriding.org