The number three appears all over in Western history and thought. The trinity is a fundamental concept to Christian theology (father, son, holy ghost), our view of time is broken into three parts (past, present, future), philosophers often break their thoughts down into "trichotemy" (Plato, Aquinas, Kant), a musical chord is made up of at least three notes, psychology speaks of three part psyche (id, ego, and superego), and all throughout other fields (art, science, geography, etc), the number 3 holds great significance.
However, perhaps the greatest significance it has, and the reason why this simple number has become so important to us, is that a traditional viewpoint of the self consists of three parts: the body, mind, and soul.