Peach is a strange colour. It's of course most associated with the fruit bearing the same name. Considering the history of color theory, it's probably safe to assume that the fruit came first and, much like orange, we began referring to that particular shade of pale, orangey-pink by the same name.
Outside of flowers, the color peach isn't that common in the natural world, but one particular bird breed more than makes up for that all on its own.