Here is the short answer for all those of you wondering: No, there is no specific group of muscles specifically designed to stabilize or create balance. Don’t misunderstand me, what I am really trying to say is all muscles work to stabilize, not some mythical group. For example, during push-ups, a triceps and pectoral routine, the biceps work to steady the arms by staying stiff thus playing the role of stabilizer.
However, there is deep muscle tissue which during traditional exercise is usually overlooked. Any exercise that is going to require stabilization will work these deep muscle. When these muscles are trained the body does not grow bulk but instead it tightens and bulls inward developing hard, cut lines. During exercises like yoga, Pilates, or dancing the deep muscle in the torso will act predominately as the stabilization muscles. This muscle group is referred to as ‘core muscle’.
Working these muscles will burn calories just as well as working your superficial (out layer) muscles. The only difference is these will not create any bulk on the body. So that makes routines and exercises that require balance perfect for people who are trying to tone their body rather than build to it.
Even if you are trying to bulk up the body, routines that require stabilization are going to create fuller more functional muscles. That is precisely why physical trainers will have you work counter routines. The whole point is to develop the muscle in a versatile manner, so that you can have the most control possible.