The inter-cooler chills each specific charge of incoming air before it reaches the turbo-charger. Cooling the air increases the air density but also the amount of oxygen in the air. More oxygen condensed into a specific quantity of air enriches the mixture of oxygen and fuel that's required for combustion and ultimately generates more power with each cycle of ignition.

This process further extends the turbo-charger's efficiency and results in virtually no detectable lag in the timing between throttle depression and actual acceleration. What you end up with is lively throttle action.