An automotive cooling system functions by sending liquid coolant, pumped through passages in an engine's block and heads to help reduce the temperatures brought on by the repeated combustion chamber explosions of the air/fuel mixture. As the liquid coolant flows through these block and head passages, it picks up heat. As it's pumped through the passages and hoses, it reaches the radiator. The radiator is the heart of an auto's cooling system. The radiator is large rectangular structure with narrow back and forth passages surrounded by narrow metal fins that help to dissipate heat as the coolant flows through it. The final part of the cooling equation is the air convection cooling of the coolant as it moves through the radiator. Fans as well as air pushed through the radiator at speed chill the coolant as it moves through it.
The radiator hoses (an upper and a lower hose) are often the most common parts of the cooling system to fail. As they're just rubber hoses, they eventually fail. The upper radiator hose flows coolant from the top of the engine (usually on the intake manifold) to the top of the radiator. The bottom hose returns the now cooled coolant to the water pump, which moves the coolant through the engine passages.
The water pump is a centrifugal pump driven by a belt connected to the engine's crankshaft which circulates coolant whenever the engine is running. The water pump simply moves water through the engine's internal block passages.
An engine's cooling fan is important component in the cooling system of an internal combustion engine. It's designed to move air through the radiator when the automobile is at low speed or stopped. It's necessary in those instances because air movement in those instances isn't sufficient to cool the fluid moving through the radiator. This air flow removes heat from the coolant created by internal combustions inside the engine. Most later model autos use radiators that are temperature controlled and only run when needed.