Cats have beautiful coats, inherited from their wild ancestors. It is this evolution, combined with genetic transfer, that has brought about the variety of colours and patterns that we see today on the fur of different breeds.
The colour and tone of your cat depend, essentially, on melanin and its two components: eumelanin and pheomelanin. It is the combination of these two - in greater or lesser amounts - that defines an animal’s colour. Eumelanin produces brown and black, whilst pheomelanin gives us red and yellow. They are combined, mixed, and result in your cat.
As happens with humans, hair colour is determined by the amount of melanin transferred genetically by the father and the mother to their young when they are conceived. That is to say that it is the sum of both genes that defines the colour of the new kitten:
Intense shades: intense colours like black, chocolate, cinnamon and red come from a gene called 'dense'.
Soft shades: grey, cream, lilac and blue are softer colours provided by a gene called 'diluted'. The red gene is unique in that it determines, depending on combinations, if the offspring is a pure colour or if they will combine intense and soft shades. The latter is what we call tortoiseshell.
White: white is the colour that prevails in genes other than those already mentioned, and it normally appears mixed with the others, given the genetic combination. It is a gene that neutralises the other colours and it is possible that it will appear as a pure colour if the right formula comes about. This gene can cause deafness, especially in white cats that have blue eyes.