The Cat's Original Coat
The cat's original coat was of color-banded agouti hair, designed for camouflage in the natural environment.
The first mutation away from hair with bands of color to a single color, or non-agouti hair, was probably to black; this mutation is often seen in other cats, such as the "black leopard" or "black panther."
Other mutations occurred for red, white, and dilution of solid colors, and all were perpetuated because the domestic cat no longer needed its wild, hunting camouflage to survive.
These few, simple genetic variations created the framework for the seemingly endless variety of coat colors that exist in cats today.