When it gets to about halfway, the fan will kick in. A heat sensor did that. The fan serves to increase the volume of air moving past the little fins. Since a car traveling at 60 or 70 mph has its own built-in airflow system, it doesn't need a fan going all the time. The water pump drives the coolant through the system.
Pumps come in several varieties, but are generally a centrifugal type, with a rotating impeller.
They're driven by a pulley off the engine. Well, a lot of things. For one, the system can spring a leak. If you notice that your vehicle is running warmer than usual, park it, turn off the engine, and look underneath. If so, open the hood.