The pigments in hair are made up of different types of melanin. The main types are eumelanin , which is brown, and phaeomelanin , which is red. Somebody with dark hair has mostly eumelanin . Somebody with very bright red hair has a little eumelanin but lots of phaeomelanin. People with auburn hair will have some of both types of melanin.
Red hair is interesting because it is particularly likely to change hue over the years. Also, it can be a bit variable over the body; notably, sometimes men with brown hairon their heads have red beards. Some blond babies turn into redheads by the age of 5, while some redhead babies fade to dull brown hair by adulthood.