Not a physiology major or anything, just a competitive distance runner, but a friend gave me this info:
The basics are pretty simple. Essentially you have two types of muscle: Type I - slow twitch, and Type II - fast twitch. There are actually two types of type II in humans - IIa and IIx - but we're mostly concerned with the later.
Slow switch fibers are also known as "red" muscle, because they are densely packed with capillaries and receive a ton of blood flow. Slow twitch fibers are also full of mitochondria and myoglobin, which makes them efficient at generating ATP (think of ATP as the energy molecule, or a charge in the batteries). Because of the constant oxygen influx, and the high presence of mitochondria and myoglobin, red muscle is able to perpetually "recharge" in a way that fast twitch muscle cannot.
Fast twitch fibers or "glycolytic" fibers by comparison are low in mitochondria and myoglobin, and do not have nearly as many capillaries, thus their white appearance. While their oxidative capacity is limited, fast twitch fibers are loaded with glycogen and creatine phosphate, from which the majority of their exergy comes. Because they metabolize ATP very quickly through this anaerobic process, they are able to contract at a much higher velocity. Unfortunately, energy stores are rapidly depleated.
The "average" person is about 50/50 between fast twitch and slow twitch. Your postural muscles - such as those in your core, neck, and calves - tend to be more of the slow twitch variety. Your genetically predisposed to the relative amounts of fast or slow twitch muscle you have; elite distance sprinters can have up to 80% slow twitch, and likewise elite sprinters can have just as much fast twitch.
You can't "change" your genetic muscle physiology, but you can nurture what you have. Regardless of your predisposition, you have to train to see the full benifit of whatever your muscle makeup is. White muscle fibers can can acquire greater levels of mitochondria and myoglobin to become more fatigue resistant through training.
So to recap:
Fast twich: Contract fast, metabolize ATP quickly, use glycogen more than oxygen, not efficient for prolonged use.
Slow twitch: Contract slow, metabolize ATP slowly, dense with oxygen and capable of processing it efficiently into ATP.
You can tearn fast twitch into slow twitch but not the other way around, once the fast twitch fibres are gone, they are gone. It is much easier and more important to work on them as you are growing.