The zapper is just a plastic casing that conveniently positions the nunchuk underneath the wiimote in a gun-like shape. With a 2-handed grip it's much easier to make pinpoint aims at the screen. Some people have mentioned how easier Trauma Center is playing with the zapper.

Is it worth the pricetag? It's up to you really. RE: Umbrella Chronicles(and others, also) is perfectly playable without it.