I think the comment regarding "Googleing" how a Turbocharger works is the right idea for you. Forced air induction is simply forcing (a.k.a. boosting or pushing) more air into the engine...and if set up properly, the fuel will also increase and you generate more HP. Supercharging is mechanically turning the blower typically with a belt drive off of the engine......reaction time is quicker, but you gain a parasitic load since the engine is driving the blower. Turbocharging uses the waste exhaust gases to spin the blower, so it's basically free power. There typically will be a lag with a turbocharger if the engine is at a low RPM and not generating a lot of exhaust flow, but once that exhaust flow starts increasing the turbo will wind up right now quick. The term spooling a turbo (the hot and cold wheels inside the blower start turning faster) simply means you are engaging the turbo with demand for more power....hit the accelerator, fuel increases, engine starts revving faster, exhaust gases increase, turbo spins faster forcing more air into the engine, revving happens quicker, you go faster. I'm no sure how fast the GT-R turbos turn at full throttle, at least 20,000 rpm one would expect. Big diesel engines in equipment typically will turn at 80,000 RPM and natural gas large engines run at 120,000 rpm.
Load factors on the engine play into how quickly a turbo will spool up. At 3000 RPM, it should react very quickly in 1st and 2nd gears and a little slower as you move higher in the gear ranges, if the car is simply cruising and you then stab it. I'm been on the highway in 6th gear and kicked the accelerator and the car reacts almost instantaneously. If you're doing that same RPM in fist or second gear and kick it, it's "right now" going to spool up....just like pulling the trigger. Boost comes on in a heart beat.
The next lesson is on aftercoolers, which the GT-R has and wouldn't be near as quick as it is, without them......