Gear-trains are incredibly simple, so I'm going to try to explain them briefly.

If your ratio is 48/16, for instance, it can be simplified to 3/1. That means that for every revolution of the cranks, the wheel does three revolutions. A 45/15 ratio would produce an identical result in terms of pedaling effort required. A ratio of, say, 40/16 means that for every revolution of the cranks, the wheel does two and a half revolutions. It becomes easier to pedal, since the effort you put in is not moving you forward as far. When you're going down a hill, however, this becomes a bad thing, since your cranks will be turning more for each wheel revolution.