Dying hair is a done from a series of chemical reactions. Ammonia opens up the cuticle and then the dye can be deposited within the hair shaft under cuticle. Then after the cuticle closes back up (cool water rinse and natural process over time) the dye is trapped. As you wash your hair the cuticle opens up and some of the dye can be removed, thus the fading of hair dye over time.

Color is determined by the reflectivity of the pigment in question. Pigments that absorb more light are darker.