How do the waters of the earth's oceans help distribute heat from one place to another?
Through the currents.
The oceans act as a sink for the solar radiation accumulating large amount of heat thanks to the high thermal capacity of the water.
Once the water becomes warmer it also becomes less dense respect to colder water. This triggers water movements originating a system of currents called "thermo-haline circulation" from the ancient Greek words indicating heat and salt.
These currents act as "conveyor belts" transporting warmer water towards colder areas at surface. The water then releases its heat, becomes denser and sinks. This originate a counter-current of cold water at depth that completes the circulation.
The most famous of such currents is the "Gulf Stream" that carries heat from the Gulf of Mexico along the eastern cost of USA and then crosses the Atlantic (becoming the North Atlantic Drift) reaching the UK and providing for warmer winters in North Europe. Once cooled the water sinks in two areas East and West of Greenland and returns towards the southern latitudes as deep oceanic current.