The water pump pushes coolant from the radiator through the coolant system, into the engine and back around to the radiator. The heat that the coolant picked up from the engine is transferred to the air at the radiator.
Without the water pump, the coolant just sits in the system. The engine is likely to overheat, which can cause serious engine damage. Water pumps have a life span and should be replaced at the interval your owner's manual suggests.