I've done some oceanography at uni. As everyone else said, if you had a specific question we could give better answers.
Yes, there are different currents like the East Australian current from finding Nemo. The Global Conveyor Belt is basically a whole bunch of currents which are connected and flow around the Earth (google it for a diagram). It transports nutrients and heat around the Earth. If it ever stopped some parts of the world could become a lot colder than they are including the North Atlantic. For example, the norther UK is warmer than average for its latitude because currents transport warm water there from the Gulf of Mexico. Another name for the global conveyor belt is the Thermohaline circulation. Thermo=temperature, haline=salt. The currents move due to salinity and temperature differences in ocean water around the globe. Cold or saline water (near the poles) is more dense than warm and less salty water near the equator. Water has lower salinity near the equator because there is more rainfall and has higher salinity near the poles because when salt water freezes the salt is pushed out of the ice. Denser water sinks, less dense water (relative to the water around it) rise. This process causes the currents. The ocean is huge so it takes around 100,000 years to complete one circulation.