Wii Classic Controller
The Wii Classic Controller is an extension or accessory for the Wii's Wii Remote. It is used for playing Classic Games on the Wii. It is also interesting to note that the classic controller has dual analog in a similar way to the PlayStation controllers. This controller can be used to play Mario classics such as Super Mario 64 and Super Mario World. It will also be compatible with Super Smash Bros. Brawl.
Just as GameCube was codenamed Dolphin, and Wii was codenamed Revolution, the Wii Classic Controller was codenamed Shell.
The reason why the Wii Remote can't be used for some Virtual Console console games is because certain consoles need additional buttons, while the Nintendo 64 games need an analog stick. Also, using a Nintendo GameCube controller can be rather hard to use, for many Super Nintendo games due to the layout of its buttons.