If you can cram more air in there, you can also inject more fuel, and
thus get more power. An air intake system with less restrictions helps,
as does taking in cold outside air rather than warm air from the engine
compartment. This is because cold air is denser than warm air, so a
cubic meter of cold air contains more molecules of O2 than a cubic meter
of warm air.

Turbos and superchargers increase power for the same reason, they push
more air into the engine. Of course turbos and superchargers these
provide a much larger power gain than a better air intake does.

In my opinion, the increase air presure/flow is not worth the bad fuel
economy. However, if the engine is already giving poor economy (e.g many
of the GM/Dawoo cars), screwing around with the air flow might result in
a better setup.

Pars

More air plus more fuel can sometimes equal more power.  Compare the cost of
the intake vs. the negligible (if any) hp increase.  Also, with some intakes
on some cars you lose the cold start function, can actually lose hp, louder,
sounds like a mooing cow in distress.