A WAD file is a file archive containing .APP files, which can be extracted and installed on a Wii gaming console. They often contain information for the Wii, such as System Menu, IOS, Channels etc. Although they are mainly used to install custom channels and IOS, they have also been linked to piracy, as users can install pirated WiiWare and Virtual Console titles through the use of WADs. WADs are generally installed using the homebrew application WAD Manager.
References
Wii WAD Wikipedia(Text) CC BY-SA