A radiator is any device that emits a form of radiation. It is also a common term for a heat exchanger of some sort. The term normally applies to one of two uses:

Automobiles

In automobiles with an internal combustion engine, a radiator is connected to channels running through the engine and cylinder head, through which is pumped a liquid, typically a water with ethylene glycol (antifreeze) mixture. The fluid is heated by the engine and then flows through a thermostat back to the radiator, where it is cooled again. This process cools the entire engine.
See also intercooler.

Buildings

In buildings, a radiator is a heating device, which is warmed by hot water being pumped into it from a water heater. Hot water enters at one end and rises to the top of the radiator. As it gives out its heat, it cools and sinks to the bottom of the radiator and then is forced out of a pipe at the other end. If there is air trapped inside the radiator, then the water cannot rise to the top, and only the bottom area gets hot. A bleed screw near the top of the radiator allows the trapped air to be 'bled' from the system, and thus restore correct operation. The air near a radiator is heated and produces a convection current drawing in cold air to heat. If setup improperly they can make loud banging noises like someone hammering on the pipes. This is due to the pipes rubbing on surrounding surfaces while expanding and contracting due to heat changes. Stereotypical radiators (as pictured) are no longer common in new construction. The current trend in radiant heating is towards floor heating, where the hot water is circulated under the entire floor of each room in a building.

Electronics

In electronics, a radiator is also known as a radiating element. Radiating elements are a basic subdivision of an antenna. Radiating elements are capable of transceiving electromagnetic energy.