Head And Eye Stabilization
Keeping the head stable serves a dual purpose – the eyes get a better view, and the vestibular organs remain level, so their sensory information is easier to interpret, making balance easier.
In humans, this latter point is especially important, because we have huge heads balanced on long vertical spines. Any deviation of the head away from a neutral position can have large effects on full body balance.
Even when we walk while looking straight ahead, the head must differentiate from the trunk to stabilize the gaze, because the trunk is rotating and tilting a little bit from side to side. As we age, the head starts to move along with trunk, which may be part of the reason we may take smaller steps and slow our walking pace down to reduce the acceleration of the head.
There are some activities where gaze stabilization points the way to good technique. In tennis and golf, one of the fundamentals of a good swing is keeping the head steady while the shoulders move.