The wand is used to focus the horse and to teach him to stay back. Also, you can move the wand between you and the horse to make an invisible barrier to define your space. Usually in a few short lessons, a horse will learn to keep in his own space and will develop a new sense of confidence and self-control. Most of us have the instinct to hold tighter and get in closer when a horse is afraid. You will find that by giving the horse his own space, there will be less for him to resist against and he will calm more quickly.
Most people find that as their balance improves so does the horse's.
Riders also find themselves more balanced, precise and focused while riding.