The explosion in a cylinder on an engine occurs when a mixture of air and gasoline confirming to a precise ratio is compressed and then you apply an electrical spark to ignite it. In order to get a bigger explosion which will make the engine make more power you must get in more air and fuel in this ratio, you can't just add fuel alone.

The turbocharger accomplishes this by using the exiting exhaust gas to drive a fan wheel that is on one end of a shaft that also has a compressor fan wheel on the other end. The compressor fan wheel is pushing more air into engine to be mixed with more fuel in order to accomplish more power production. The amount of exhaust gas exiting engine is a product of how hard engine is working. If you drive easy on level ground the turbocharger is not pushing any additional air and the turbo is effectively not working. If you depress throttle then the exhaust gas volume will increase proportional to how hard you push throttle and the turbo will push additional air in that same proportion.

The speeding up of the turbo to the speed at which it produces additional air flow takes an amount of time that varies a bit depending on when you get heavy into throttle. From a standing start it make take 1 -1.5 seconds but it may be only a few thousands of a second at higher engine speeds. On a 94 850 turbo the turbo charger's effect doesn't become really noticeable until approximately 2400 rpm.