The Nunchuck is the controller that comes with the Wii and is used for 3D navigation games (most of the time), such as Super Mario Galaxy. The nunchuck has 2 buttons, a joystick, and a cable to plug into your Wii Remote; the two buttons are the Z button and the C button. The Nunchuck happens to have sensors integrated inside the controller. The main use of a Nunchuck is to play Mario Kart: Double Dash!! on a Wii without having to use a Nintendo GameCube (controller). It can also be used to play Mario Kart Wii.
An article on the Wii Nunchuck: