One can think of global ocean conveyor belt as the movement of warm surface water towards the poles and the movement of colder water (near the ocean floor) towards the equator. This constant motion of ocean water takes place around the globe and moves the heat around the planet, thus forming a gigantic conveyor belt. This motion of ocean water keeps certain regions warm and others cold. One famous example of such current is the Gulf Stream. It carries heat to northwestern Europe and keep it warm, while keeping Florida and other regions of northeast US colder. The motion of salty ocean water depends upon its density.
With the climate change, polar ice caps are melting and this is causing freshwater (from snow melt) flow into seawater. The retreating glaciers are also exposing more sea surface, thus causing enhanced evaporation and subsequently, higher rainfall. This may cause a decrease in salt content and hence the density of water. This will likely result in lesser ocean currents and hence will impair the global conveyor belt. If this were to happen, heat distribution will not take place and places such as northeastern Europe will become much colder, while northeastern US will become warmer. Similar changes are expected throughout the world.
Hope this helps.