A "wiki," according to the folks over at WikiWeb, is:
A wiki is a collaboration tool - a web site where the pages can be changed and INSTANTLY published using only a web browser (no programming required). Pages are automatically created and linked to each other.
I like to think of it as an online manual, which anyone (or anyone with permission) can update at any time. It's a way to organize and share information. Wikis are usually formed around a central idea, and are a good "host" for volumes of information, such as Judgepedia, which focuses on courts and judges, and Dr. Rahn's Supply Side Wiki, which focuses on supply-side economics, or this Simpson's wiki, which focuses on the popular TV series. And then there's the Uncyclopedia, which is a funny, fictional spoof wiki.
MediaWiki is the software used for the popular "Wikipedia," which is an online encylopedia updated by users. This software takes some learning and practice. Alternatively, I have recommended WikiSpaces for my clients, because of its WYSIWYG (What you see is what you get), editor, which requires very little "learning" of code.
For more information, Common Craft has a great video, Wikis in Plain English.
Jennifer Pointer (e-mail) is in Tulsa, OK. She promotes a simple, a low-tech approach to effective online profile management, search engine optimization and social networking.