The radiator needs a constant flow of air through its core to cool it adequately. When the car is moving, this happens anyway; but when it is stationary a fan is used to help the airflow.
The fan may be driven by the engine, but unless the engine is working hard, it is not always needed while the car is moving, so the energy used in driving it wastes fuel.
To overcome this, some cars have a viscous coupling a fluid clutch worked by a temperature sensitive valve that uncouples the fan until the coolant temperature reaches a set point.
Other cars have an electric fan, also switched on and off by a temperature sensor.
To let the engine warm up quickly, the radiator is closed off by a thermostat, usually sited above the pump. The thermostat has a valve worked by a chamber filled with wax.
When the engine warms up, the wax melts, expands and pushes the valve open, allowing coolant to flow through the radiator.
When the engine stops and cools, the valve closes again.
Water expands when it freezes, and if the water in an engine freezes it can burst the block or radiator. So antifreeze usually ethylene glycol is added to the water to lower its freezing point to a safe level.
Antifreeze should not be drained each summer; it can normally be left in for two or three years.