What keeps a satellite in orbit?

If one really studies a satellite then one can tell that it is not necessarily in a fixed orbit, but is in a type of controlled 'fall'. When it is launched into space gravity pulls it slowly back to Earth. But, by moving fast enough the fall becomes a spiral instead of a steep drop. If for some reason the satellite does not maintain its speed, it will burn up in the earth's atmosphere. It is a balance of speed and gravity.