A flywheel is an energy storage device. To accelerate it up to a given speed in a given time requires a fixed amount of power. Reduce the weight of the flywheel (or more accuracy reduce it's moment of inertia), and for the same power input you reach the same speed more quickly.
A lightened flyweel can give worthwhile performance improvements in lower gears, where the flywheel is a significant fraction of the total load on the engine. The advantage drops off in higher gears, since the load of the mass of the car swamps the effect of the flywheel.
One thing to bare in mind; a badly modified cast flywheel is basically a fragmentation grenade. The damage they can do if they explode at high RPM is frightening, the parts will slice through bellhousings and thin steel body panels like butter. A billet steel item should always be used if you want to save a significant amount of weight.