As Squiffy said, a pre-amp controls the inputs (selection and volume, maybe tone, balance, digital to analogue conversion, digital processing, etc.), and a power amp boosts the signal to drive the speakers.
Most amplifiers and receivers are integrated, which means that they combine pre- and power amps inside one case, with a common power supply. Some integrated amps have pre-outs, so that you can add a separate power amp.
As you spend more money, you get separate pre- and power amps. The idea is that sound quality is improved by separating the low-level signals in the pre-amp from the high-level signals in the power amp. This works because the components are isolated inside separate metal boxes, and they each have their own power supplies.
Some source components, such as CD players, effectively have pre-amps built-in - they have volume controls, so can be connected directly to a power amp.