The iris is the coloured part of your eye. It serves to control the amount of light that gets inside, protecting the sensitive retina. It is a thin (~1 mm), donut shaped ring of muscle fibers that change the diameter of the hole in the center of it, called the pupil.
Operation of the iris is simple. When light levels increase, it will constrict the pupil. When light levels decrease, the pupil will dilate. The objective is to keep the amount of light entering the eye as constant as possible.
The iris' colour and texture are the result of pigment cells. To be more specific, eumelanin produces black, and pheomelanin produces red. These two pigments combine in varying amounts to form wicked cool patterns that are unique, like your DNA or fingerprint. The pupil is black because the retina, at the back of the eye, has pigments in it that absorb light.