A forced induction system overcomes the limitations of atmospheric pressure by pushing more air into the cylinders. Consequently, the engine’s power output becomes a function of how much boost it gets. What’s more, dialing up the boost pressure overcomes a lot of deficiencies in the induction system and cylinder heads that would otherwise limit air flow and the engine’s volumetric efficiency.
After all, it is much easier to push air into an engine with a turbo or blower than to suck it in with intake vacuum alone.
Even with a relatively moderate amount of boost, say 6 to 8 psi, a forced induction system can easily increase the power output of a typical street engine 150 or more horsepower.
Nitrous oxide injection also serves to boost power by cooling the intake charge. Nitrous is stored in the bottle in liquid form at about 1000 PSI. When it is released into the intake, it expands into a gas. This causes the temperature to drop considerably, which causes the density to rise. The denser the intake charge is, the more that will fit in the cylinder.
Interestingly, the use of nitrous oxide as a performance enhancement has been traced back to World War II, where it was employed to give both Luftwaffe and Allied aircraft "emergency" boosts in both airspeed and altitude capabilities. However, with the advent of jet propulsion at the end of WWII, the government's interest in piston-powered aircraft waned. And for the most part, nitrous R&D was shelved.