As was described a powerhead is a small water pump that is used most commonly to circulate the water within the tank. These pumps sit in the tank to move water around. In the natural reef the water is very tirbulant so having a tank with no powerheads and effectivly very low water movement is not replicating the natural habitat.
can act as a filter if you have a prefilter on the intake of the powerhead. This will filter small particles out of the water that go into the powerhead and the prefilter will provide a surface for benifical bactera to grow.
The water movement is needed to keep fish waste from collecting on the rocks and corals if you have any. In addition most corals are filter feeders in that they get their food by collecting it from the water column. If the water is not circulating then they can not get the food.
For a 30 gal
tank you should have at a minimum 300GPH water flow in the tank. Ideally I would shoot for something like 450GPH.