if you placed an air-to-air intercooler into your intake plumbing without a supercharger/turbocharger, then you are just cooling your intake air with ... air at the same temperature - no net gain here. Worse, you will also be introducing unnecessary restrictions into your intake plumbing, which will limit air intake.

like what the other members have mentioned, the intercooler is a heat exchanger which removes heat from intake air that is compressed by some form of compressor (engine-driven or exhaust-driven). Exhaust-driven turbochargers impart more heat into the intake charge because of the exhaust heat conducted into the compressor housing (compared with an engine-driven supercharger).

you want this excess heat removed for 2 reasons:
* a cooler charge will be denser, permitting more air/fuel to enter the cylinder, for more power
* a cooler charge decreases the chances of detonation