Basically, with a 2-stroke, you’re doubling the number of power strokes (actual gas combustions) per number of engine revolutions, so you get twice the oomph for the same number of revs.
When MotoGP first allowed 990cc 4-strokes to compete with the traditional 500cc 2-strokes in 2002, they were expected to perform about evenly. Unfortunately for the 500cc riders, the 4-strokes ended up with more horsepower and, thanks to their more even power deliver (2-strokes can be…unpredictable), more power to the wheels out of turns. The 4-strokes ended up dominating with horsepower figures approaching 250hp, despite being MUCH heavier than the 2-strokes (though still lighter than my DR-Z…mindblowing innit?). The 250cc GP class has been replaced in the coming 2010 season by the 600cc 4-stroke “Moto2” class. So the 2x 2-stroke to 4-stroke cc conversion is only a rough “guesstimate.”
Incidentally, since 2002 when they switched to 4-strokes, engine displacements have been reduced to 800cc (2007-present), and are going to be increased again to 1000cc in 2012.