On a turbocharged car it is prior to cool down the compressed air to achieve good performance. A bigger intercooler means more efficient cooling and better performance, but also more reliability.
Intake systems are replacing the original air filter box to improve the air flow into the engine. By upgrading the intake system the engine will be better fed with fresh air which means better results in power and torque. Higher power values are then reached.
The original air filters are mostly made in paper. Very restrictive and not the best way to get power from your engine. A better air filter will allow the engine to breathe easily and with a better filtration.