What is a wiki?
A wiki is a web site which uses a simple web interface for editing. Open wikis can be edited by anyone and the simple editing interface means that there is no need to learn to use an application such as FrontPage or Dreamweaver. Probably the most widely known example is Wikipedia, the free encyclopedia. This book is also using wiki software.
History of wikis
Wiki software originated in the design pattern (computer science) community as a way of writing and discussing pattern languages. The Portland Pattern Repository was the first wiki, established by Ward Cunningham on March 25, 1995.  He invented the wiki name and concept, and implemented the first wiki engine. Some people maintain that only the original wiki should be called Wiki (upper case) or the WikiWikiWeb.
Cunningham coined the term wiki after the "wiki wiki" or "quick" shuttle buses at Honolulu Airport. Wiki wiki was the first Hawaiian term he learned on his first visit to the islands, when the airport counter agent directed him to take the wiki wiki bus between terminals. According to Cunningham, "I chose wiki-wiki as an alliterative substitute for 'quick' and thereby avoided naming this stuff quick-web." 
In the late 1990s, wikis increasingly were recognized as a promising way to develop private- and public-knowledge bases, and this potential inspired the founders of the Nupedia encyclopedia project, Jimmy Wales and Larry Sanger, to use wiki technology as a basis for an electronic encyclopedia: Wikipedia was launched in January 2001; it originally was based upon UseMod software, but later switched to its own, open source codebase, now adopted by many other wikis.
In 2005, the Los Angeles Times experimented with using a wiki in the editorial section of its web site. The project was quickly shuttered as vandals quickly defaced it and features to help distribute administration of the site had been disabled.
Today, the English-language Wikipedia is, by far, the world's largest wiki; the German-language Wikipedia is the second-largest, while the other Wikipedias fill many of the remaining slots. The fifth-largest wiki is Susning.nu, a Swedish-language knowledge base running UseMod software. The all-encompassing nature of Wikipedia is a significant factor in its growth, while many other wikis are highly specialized. Some also have attributed Wikipedia's rapid growth to its decision not to use CamelCase.
From Wikipedia w:Wiki
- A community developed documentation project. 
- Web pages which are editable by visitors to the website as opposed to conventional websites which can only be changed by the webmaster. Usually used for "community" or technical sites to allow for joint authoring and ownership. 
- online collaboration model and tool that allows any user to edit some content of webpages through a simple browser. 
- A Wiki or wiki ... is a website (or other hypertext document collection) that allows users to add content, as on an Internet forum, but also allows anyone to edit the content. "Wiki" also refers to the collaborative software used to create such a website. w:Wiki
- See also: wiki:WikiDesignPrinciples
Free hosted wikis
Open Source software
Using wikis in teaching and learning
- WikiSchool - ideas for using wikis in the classroom 
Here are some resources specifically about using wikis in education.