What purpose does an intercooler serve?

It is quiet simple, it cools the air that is compressed by the turbocharger or supercharger

A turbocharger is nothing more than a air compressor, in simple terms. What is quite unique about a turbocharger is that it uses the exhaust gases from the engine, to compress the intake charge. The turbine which is the driving force behind the turbo, is driven by the hot exhaust gases from the engine. The turbine wheel can spin at speeds in excess of 150,000rpm. On the same shaft the compressor wheel is driven by the turbine wheel, whose it's job is to compress the intake air. When air is compressed, it heats up by a great amount. The inlet temperatures can reach in excess of 200 Degrees Celsius.

This is where the intercooler comes in. The intercooler cools the air that is compressed by the turbocharger or supercharger. The colder the air entering the engine, the greater the density of the oxygen rich air, and the more power the engine produces. Thus cooling the intake charge air, allows you to turn the boost up higher on your performance machine. Not to mention increasing the longevity of the engine itself.

Intercoolers reduce thermal stress on the engine

A performance engine undergoes much punishment through it's life. Turbo charged engines are built extra tough, not only to cope with the much larger power output, but to be more resilient to thermal stress. Intercooler's reduce thermal stress. Thermal stress is caused by very rapid change in temperatures, just like when a turbo comes on boost under full load. The inlet temp can go from 60deg C to 160deg C in a matter of seconds. Since the intercooler keeps the inlet temperatures down, this helps to reduce the overall thermal stress on the engine.