What makes eye colour?

Eye colour is determined by the amount and type of pigments in the iris and phenomena such as the diffraction of light. The genetics of eye colour are complicated, and colour is determined by multiple genes.
In mammals, there are many variations in eye colour: blue, brown, grey, green, and others.
Avian eye colours range from dark brown and yellow through red, blue, and green to metallic silver and gold. In some species, eye colour differs between the sexes.
The superficial (stromal) layers are richly supplied with blood vessels and contain scattered cells with pigment granules. The deepest (epithelial) layer of the iris contains large amounts of dark pigment (melanin). 
Blue eyes have the usual deep epithelial layer full of dark pigment but the upper layers are thin and have little or no pigment granules. White light is made up a spectrum of colours. The red wavelengths penetrate and are absorbed in the epithelial layer. The blue wavelengths are scattered by the sparse pigment granules and the iris appears blue.
Brown eyes have lots of pigment granules in the superficial layers and the pigment cells are closely packed. This absorbs most light and the eye appears brown.
Hazel, green and grey irises have progressively less stromal pigment and so show colours in between blue and brown.
The brightly coloured eyes of many bird species are largely determined by other pigments, such as pteridines, purines, and carotenoids.
Albino animals are unable to make the dark pigment melanin. The iris colour is pink as the rich stromal blood supply provides the colour.
Heterochromia is a condition in which one iris is a different colour from the other iris. It usually results due to uneven melanin content and may be inherited or acquired by disease or injury.

Heterochromia

Albino iris