Most stock air boxes and filters have quite a bit air restriction when the intake manifold sucks in the air. To achieve the maximum power from your engine, it basically needs a good amount of airflow. But not that only, the air has to be cool as cold air is denser than hot air, so more of it can be packed in the combustion chamber, which then would give you more power with the same amount of throttle response.
Turbo's also do the exact same thing, except that the air pressure is really high, so it's measured in PSI. The only difference why a turbo charged ride drinks more fuel is because firstly, it's run by the exhaust gases, which does put a little load on the engine, but mostly it's because at that rate of air flow, larger injectors which are usually pre-installed, now spray more fuel into the engine, making it burn more fuel. MAF/MAP sensors can only measure a certain amount of air flow, specially MAF sensors, till a certain extent as the speed of air that a turbo gives an engine just throws it off it's values, making it usually run richer or in other words throw 'black smoke' from the tail pipe.
You guys must have seen vids where a really high powered Supra or Evo throws black smoke down the tail pipe, usually at launch. Well it's the same reason that proper air/fuel ratio within the combustion chamber cannot be attained as the air is just too fast for sensors to give a proper value. O2 sensors come in handy in such situations, but they only work once the engine is a bit warm and they don't give precise readings.
I've installed intake, took me a while, but take some pics tomorrow morning.