The water in our world's oceans is always moving - pulled by tides, blown by waves, and slowly circulating around the globe by the force of the Great Ocean Conveyor Belt (aka thermohaline circulation). The Conveyor is powered by differences is water temperature and salinity, and one of its most well know parts, the Gulf Stream, is what gives Europe it's relatively mild climate.
Simplified diagram of the Great Ocean Conveyor Belt, courtesy of the Arctic Climate Impact Assessment (ACIA), "Arctic Climate Change and Its Impacts" report.
How it works
Warm salty water from the Gulf Stream is cooled when it reaches the North Atlantic. It becomes denser and sinks to deeper layers of the ocean, 'pumping' cold water south in the deep ocean, past Africa into the South Atlantic. Salt rejected as sea ice forms also increases the density of these waters and contributes to the process.
The dense, cooled water becomes part of what is called the Ocean Conveyor, and the water eventually returns to the surface in the Indian and Pacific Oceans. As warm water returns to the Atlantic, the current moves pole-wards as the Atlantic Gulf Stream and North Atlantic Drift, warming northwestern Europe substantially.
Aside from keeping Europe warm, and playing an important role in the global climate, the Conveyor provides an up welling of bottom ocean nutrients, and increases the oceanic absorption of carbon dioxide. The Gulf Stream is what moderates European climate, the whole system is called The Great Conveyor Belt, the Great Ocean Conveyor, or whatever other popular name you want to give to the thermohaline circulation system.
What could go badly wrong
Worryingly, recent studies warn that we may already have evidence of a slower Conveyor circulation over the Scotland-Greenland deep ocean ridge. And while the Conveyor appears to have operated fairly reliably over the past several thousand years, an examination of ice cores from both Greenland and Antarctica shows that this has not always been the case. In the more distant past, changes to the Conveyor circulation are associated with abrupt climate change.
In short, dilution of the ocean's salinity - from melting Arctic ice (such as the Greenland ice sheet) and/or increased precipitation - could switch off, slow down or divert the Conveyor. This dramatic cooling would mean a massive disruption to European agriculture and climate, and impact other sea currents and temperatures around the globe.