Hi Mark,
When clipping a climbing rope/ropes into protection, the idea is mostly to have the rope travel in a more or less straight line between protection points. This minimizes rope drag, a real pain in the ass when you're above your last piece/clip, trying to pull up rope to make the next one and it feels like there is a bag of cement on the other end.
When climbing sport routes, you usually only use one rope because the bolts on a well bolted climb will be placed so that your rope runs straight (you'll see special notes for particular routes, something like "a long draw on the third bolt prevents death", "pre-clip the second bolt to prevent rope drag").
When climbing trad this is often not possible, unless you're climbing at Indian Creek. To counteract your rope running in continuous ZZZZs up after you, you use a
half (sometimes called double?) rope system, where each rope is thinner (8 - 9mm) than a normal single rope. You tie into both and when a piece of pro is out left, you clip rope A, similarly, when a piece of pro is out right, you clip rope B. The advantage is that you are clipped into all the gear you've placed while having less struggles with rope drag.
Another system where 2 ropes are used is the
twin rope system, where you use two ropes but clip both into all pieces of pro. This is not very often used, but is useful when there are chances of a rope being cut due to rockfall, for instance. This doesn't help with rope drag, but adds safety.
Important thing to note:
With a single rope, you can abseil max half of your rope length. With either of the double rope systems, you tie the two ropes together and can abseil the full length of the ropes. Saves time by halving the amount of abseils to get down off a multipitch. Just make sure you don't abseil past anchors and then don't have enough rope to get to the next set. Get yourself a pair of prussiks, or a shunt or at least one ascender.
Tie knots in the end of both ropes.
Definitely check out
http://www.abc-of-rockclimbing.com/howto/ropesystems.asp