The Answer:
Dark meat is the result of active muscles.
White meat is the result of less active muscles.
The Explanation:
Chickens and turkeys use their leg and thigh muscles (active muscles) more than they use their wing and breast muscles (less active muscles).
Since chickens and turkeys only fly short distances, typically from ground to perch, they rely on their legs and thighs to get them around. The active muscles in the legs and thighs of chickens and turkeys are full of blood vessels that contain myoglobin (or muscle hemoglobin), which delivers oxygen to the muscles. The more myoglobin the muscles contain, the darker the muscle. There is no need to have a rich supply of oxygen delivered to the less active muscles like the wing and breast muscles.
Scientists refer to the active muscles as slow-twitch fibers, and the less active muscles (or well-rested muscles) as fast-twitch fibers.
Slow-twitch fibers are built for endurance, which allows the muscles to work for long periods of time, so chickens and turkeys can run around all day without getting tired.
Fast-twitch fibers are designed for quick bursts of energy, but they fatigue quickly. Fast twitch muscles are fueled by glycogen (carbohydrate stored in body tissues) giving the muscles that immediate explosion of energy needed to move rapidly.