An active cooling system is one that involves the use of energy to cool something, as opposed to passive cooling that uses no energy.
Such systems circulate a coolant to transfer heat from one place to another. The coolant is either a gas, such as in air cooling of computers, or a liquid such as in a car engine. In the latter case, liquid is pumped to transfer heat from the engine to the radiator, which in turn is cooled by passing air over it.
Other active cooling systems make use of a refrigeration cycle.
References
Active cooling Wikipedia(Text) CC BY-SA