The purpose of the iris is to limit the amount of ight that goes into the eye (letting in more light in dim illumination and less when there is a lot of light.). It does this by constricting in bright light and dilating in dim light. However, without pigmentation, the iris could not perform this function because the light would pass right thru it. This is why albinos are extremely photophobic. They have no pigment at all in their iris and light goes right thru it.
Notice how this Albino child's eyes appear to be red because you're seeing a reflection of light off of his retina right thru his iris.
Now, any normal person has enough pigment (mostly on the back or posterior of the iris) to perform this funtion. Variations in eye color come from variations in the amount of pigment present in the anterior surface of the iris.
I would assume that any variations in pigmentation beyond that necesary for the iris to perform its function is "just for show" and serves as some kind of group identifier or mating display.