We tend to think of the weather as a completely atmospheric happening, all cloud and wind and storm flowing across the face of the planet, forming new patterns every day or hour. Kind of hard to believe how quickly we forget the oceans' part in this as well, with their coverage of area and fluidly dynamic nature so much resembling the sky and wind. Still, the oceans are a complete half of the equation, the batteries powering weather's churning engine, and the Great Ocean Conveyer Belt is their most important inner system.
Think of the conveyor as a transport loop that moves water, and with it heat and carbon dioxide, through all of the oceans. To describe it as simply as possible in text, we'll say it starts in the Pacific Ocean, where cold air is fed under Australia from closer to Antarctica, and then across the equator and around in a loop. It then crosses itself (possible because each stream travels at a height concordant with its temperature, hotter water closer to the surface) and goes over Australia, and eventually below Africa. From there it travels along the Western African coast, then crosses and passes over the North coast of South America. From there the stream travels back across the Atlantic toward Europe, then bounces off Greenland and begins going South again. Between the equator and the European turnaround the conveyor drops all of its heat and CO2, letting it sink to the ocean floor instead of floating toward the top. The cold water moves all the way south around Antarctica, and then back into the Pacific ocean as mentioned at the beginning of this paragraph. There is also a subloop of water which starts near Antarctica and then moves through the Indian Ocean, warming up and finally merging with the stream which will then cross South of Africa.
Probably the most important part of this system is the Gulf Stream, the warm water which flows beside the East coast of North America and the West Coast of Europe. It carries the equivalent of 75 Amazon Rivers worth of water (or so I've read) and exchanges enough heat with the atmosphere to warm all of Europe. The gulf stream is what allows London to have warmer winters than New York, despite being more than 400 kilometers to its North. Actually, as far as I can tell, the Gulf Stream heat exchange is the only part of the system that affects land temperatures to a great degree -- actually, to roughly 5 degrees Celsius, which would be the negative difference in air temperature if it didn't exist.
The scary thing is, there's a possibility that it might in fact cease to exist in the near future. Because more fresh water is entering the ocean from melting glaciers and other ice, the salinity of the water is decreasing overall. When water becomes less salty, it also loses density, which means it will not sink as low when cold, as there is saltier, colder water beneath it. It follows that if the water cannot sink, the system of loops which cross each other will not be able to continue functioning -- the great ocean conveyor belt will come to a halt, and with it the Gulf Stream. This change, in theory, can happen in the span of five to ten years, as the system shifts more quickly with some added inertia. If you think El Niño has caused some global chaos and done some economic damage, you ain't seen nothin' yet.
While this almost certainly would be disastrous to Europe, it has happened in the past (though without the aid of the greenhouse effect), and won't drastically endanger the human species or anything. For instance, the last halt to the conveyor is theorized to have happened about 500 years ago. At that time, wine manufacture in Greenland (!) became impossible due to lessened temperatures, and some settlements there were abandoned. Famine also swept Ireland and France, due to harsh conditions stopping the growth of wheat and potatoes. That time the cycle restarted itself in a mere 200 or so years, but the North Atlantic cooling of 12800 years ago, known as the Ice Age, lasted 1300. If the shutdown happens in our lifetimes -- and that is certainly a possibility -- there is little doubt that our grandchildren and theirs will still be dealing with its effects.