Turkey meat, like all meat, is really just different kinds of muscle. Muscle is made up of fiber tissues, which, in turn, are made up of cells. In turkeys (or chickens or pigeons or any other bird ), fiber tissues have a mix of red and white cells, depending on the type of muscle. Muscles with more red cells contain a lot of myoglobin and iron, which also makes the meat darker.
Because myoglobin brings oxygen to the muscles, there's a lot of the pigment in the legs and the meat is darker. The breast meat of the turkey needs very little oxygen so there's no myoglobin. That's why breast meat is white.