The purpose of an intercooler (charge air cooler) is to cool the high pressure, high temperature air coming out of the turbocharger to make the air more dense, increasing engine power when mixed with the proper amount of fuel.

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Intercoolers are used to cool air after it is compressed by the turbocharger. When air is compressed, its temperature rises; cooling it lowers its temperature, which makes the air denser. Denser air means more oxygen molecules enter each cylinder intake stroke, so with the correct amount of fuel, more energy can be released in the combustion process and more power can be produced. The statement captures this sequence: cooling the high-pressure, high-temperature charge air to increase density, enabling greater power when fuel is properly metered. While cooler charge air can help with efficiency and sometimes emissions indirectly, the primary purpose is to increase air density for more usable fuel combustion, not mainly to reduce turbo lag.