Boost is positive air induction into the engine. This can be done with a supercharger or Turbo Charger. Superchargers are mechanically drive by an engine and Turbo Chargers for drive from the exhaust exiting the engine.
More air in the engine and you can burn more fuel completely.
Example, you put in big injectors and go out and floor the throttle, you get a big cloud of black smoke until the Turbo Charger comes up to speed and forces extra air into the engine, now with the forced air (boost) you can burn the fuel completely and the smoke goes away.
SNOKING
BTW SNOKING has nothing to do with what comes out my tail pipe.