Red meat is red because the muscle fibres which make up the bulk of the meat contain a high content of myoglobin and mitochondria, which are coloured red. Myoglobin, a protein similar to haemoglobin in red blood cells, acts as a store for oxygen within the muscle fibres.
Mitochondria are organelles within cells which use oxygen to manufacture the compound ATP which supplies the energy for muscle contraction.
The muscle fibres of white meat, by contrast, have a low content of myoglobin and mitochondria. The difference in colour between the fleshes of various animals is determined by the relative proportions of these two basic muscle fibre types. The fibres in red muscle fatigue slowly, whereas the fibres in white muscle fatigue rapidly.
An active, fast swimming fish such as a tuna has a high proportion of fatigue-resistant red muscle in its flesh, whereas a much less active fish such as the plaise has mostly white muscle.
The colour of meat is governed by the concentration of myoglobin in the muscle tissue which produces the brown colouring during cooking.
Chickens and turkeys are always assumed to have white meat, but free-range meat from these species (especially from the legs) is brown. This is because birds reared in the open exercise and become fitter than poultry grown in cages. The fitter the bird, the greater the ease of muscular respiration, and hence increased myoglobin levels in the muscle tissue, making the meat browner. All beef is brown because cattle are allowed to run around in fields, but pork is whiter because pigs are lazy. 