A car's radiator does its job of cooling the engine by forcing the coolant/water mixture through the cooling system and into the engine in a cycle, bringing the coolant temperature down before cycling it back around. It performs this task with pressure built up once the engine is running and warm.
If there is a leak in the radiator or other portion of the cooling system, the coolant level will drop, and the radiator's pressure can drop low enough to render it unable to cycle the coolant.
The radiator hoses carry the coolant into and out of the engine. If the hose carrying the coolant out of the engine breaks, the coolant will not go back to the radiator and the engine will not remain cool.
If the radiator cap has a tear in its rubber seal, the radiator will have problems maintaining enough pressure to cycle the coolant.
