The way it works is that the Capt and F/O have different air data sources (i.e. pitot/static ports). One of those may be blocked (by a tape for instance) and cause errorneous airspeed indications on one of the airspeed indicators, while the other shows good values. The problem is that it may sometimes be difficult to recognise which one is good, which, since the airspeed is vital for safe flight, may be fatal. Actually - at least two airplanes (both were Boeing 757's) have stalled and crashed because of errorneous airspeed indications. Now, on most airplanes pilots should compare the speed indications at certain speed (usu 80 Kts) during takeoff run, and if there's a disagree - they must abort. In the air, if this happens, the pilots should fly manually, using typical power settings and attitudes and identify the wrong indicator (eg. by comparing to the third - standby indicator) and use the good one.
Hope I explained it well