A turbo takes time to build pressure because it uses exhaust as a operator and pressure takes time to build. If you have ever driven a turbo'd car, you mash the pedal and it takes a half second or whatever for it to really start moving. The lag is the time between when you press the pedal and when pressure it built and it boost is gained. Thats about how can i summarize it.
In a supercharger, it is driven by the belts. The power instantaneous and you won't ever notice a lag of any sort.
It is the time from when you push the gas pedal the engine produces enough hot exhaust to spin the primary impeller which thus turns the shaft for the secondary compressor impeller. After all that it still has to compress in the incoming charge to gain boost all of this causes a lag and dependant on engine size, closeness to exhaust and weight of impellers will determine how much lag. What manufacturers have done was use a secondary smaller turbo to spin the big turbo up prematurely to help reduce the lag. Most lag is noticed in everyday driving and in drag racing the engine spends most of its time at the upper rpm range so lag is greatly reduced...Polo.
oh course it all depends on a lot of variances .. distance the air has to travel, amount of bends, size of the turbo (bigger = more lag), type of spool wheel (twinscrool = no turbo lag) .. then you got the dual small turbos which have very little lag.. 1 small turbo = little lag and little torque but if you have two your torque is back with still a small amount of lag