Types
Surface currents involve the motion of water down to 1300 feet below the surface--only about 10 percent of the total water in the ocean. Thermohaline currents, on the other hand, are slower than surface currents and move water in the ocean's depths.
Function
Surface currents are driven by wind caused by uneven heating of Earth's surface and the Earth's rotation. The equator receives more solar energy annually than the poles; hot air rises while cool air sinks, so this temperature difference creates wind circulation patterns which become deflected by Earth's rotation (the Coriolis effect). Strong persistent winds over the open ocean drive surface currents. Thermohaline currents, by contrast, are caused by differences in temperature and salinity. Cold, salty water sinks towards the ocean floor, while in other areas with higher temperatures the water will slowly warm and rise.
Significance
Ocean currents are important for climate because they help redistribute heat from the tropics to other areas of the globe. Belfast, for example, is just as far north of the equator as Ontario's Polar Bear Provincial Park, and yet Belfast has a much milder climate. The heat transferred by currents in the Atlantic Ocean is responsible for the difference.