Let's contrast stability with balance. For our PE purposes, and contrary to popular speech,"balance" is not achieved by standing easily on one foot, unless it can be as easily done on the other foot. "Balance" is the achievement of equilibrium on both (or more) sides. A baseball pitcher, for instance, develops one arm to throw strikes but will very likely be unable to even throw to the catcher with the other hand. The pitcher's development is therefore unbalanced. It is more productive to consider the achievement of easily standing on one foot as "stabilizing on one foot". The human body has over 700 skeletal muscles, many of which are used as (and informally called) stabilizers. It is not really common to refer to any of the skeletal muscles as "balancers". To strive for balance, we will consistently do all of our dancing to the left and to the right; we will rotate clockwise and counter-clockwise; we will stabilize, leap, and turn on one foot, and then the other. Think of the balance you used in chemistry labs- balance is the achievement of equilibrium on both (or more) sides.
We speak of a sense of balance (we have many more than just 5 senses), formally called equilibrioception, a sense from our vestibular system. But stability comes from proprioception- our sense of our bodies' relative position in space (the sense State Police test on erratic drivers)- and a strong, balanced, smart development of bones and muscles. Stability is also the flip side and enabler of mobility.
If the baseball pitcher does not stabilize the feet, ankle, and core, the throwing arm has no anchor, no power, and the movement will not satisfy its intention. If the dancer does not stabilize one leg, she will collapse to the floor when she tries to lift her other leg, pirouette, leap, or even walk. Some parts of the body are designed for mobility, some are designed for stability. In ballet and in PE, we will try to maximize both.
Keep Moving,
Matthew Smith