Most people are either naturally left eye dominant or right eye dominant, but some people are neither. When a person has both eyes open, the brain will subconsciously prefer the sight of one eye over the other when focussing on something - eye dominance. This is independent of whether they are left handed or right handed.
In archery and other target based sports e.g. clay pidgeon shooting, this allows you to aim the sight at a target and hit it. From eye dominance, we can ensure that you shoot with either a left-handed bow (sight and technique aligned to your left) or a right-handed bow (sight and technique aligned to your right). People with neither preference can choose either bow type for comfort while some competition archers will wear an eye patch to assist with aiming.
Sometimes it takes time for the person and Club to determine the true eye dominance of the brain. It usually manifests itself with the archer hitting another target from the one they were aiming at!