Upwelling is a phenomenon that brings cold, nutrient-rich deep water to the surface. In the Northern Hemisphere, upwelling occurs on west coasts when winds are blowing north to south. Ekman transport and the Coriolis Effect make the coastal waters move, on average, 90 degrees to the wind. This means the water near the coast is being pushed west, away from the coast. This, in turn, pulls deep water up to the surface to replace the original surface water.
Upwelling can also occur at the equator. When the north and south trade winds meet, coming from opposite directions, they push water away from the equator, which pulls up the deeper water to replace it.
Downwelling can also occur, if the winds were to reverse. Ekman transport and the Coriolis effect would cause the water to basically "pile up" on the coast and eventually sink to the bottom.
Upwelling is important for coastal communities because deep water has more nutrients. Coasts with more upwelling usually have more phytoplankton and algae growth. The deep water brought up is also colder than usual surface water, which is why, for example, the west coast of North America has much colder water, as well as lots of fog, cooler weather, and no hurricanes.
Diagrams of upwelling and downwelling: http://oceanmotion.org/html/background/upwelling-and-downwelling.htm
More information and a diagram for ekman transport: http://oceanmotion.org/html/background/ocean-in-motion.htm