The term was invented by Ward Cunningham in 1995. He used the term 'wiki' after riding on quick buses or 'wiki wiki' at the Honolulu Airport. The word wiki (WikiWikiWeb) comes from the Hawaiian word for quickly. According to High Tech Learning, a wiki can be created when a virtual collaborative team quickly constructs an interactive website.
An interesting explanation of a wiki can be found on YouTube, Common Craft, Wikis in Plain English.