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There are many aspects of a wiki, so I'll describe the ones that are important to me:
From a consumer perspective, a wiki is a tool that lets people create and edit documents via a web browser. Those documents are written using a simplified text format…no word processor required. The advantage to the simplified format is that new users can become contributors very quicly, and experienced editors can do advanced markups with very little work.
From a technology perspective, a wiki is ”the simplest online database that could possibly work”1). Its not a relational database, or even a flatfile database. Either one would imposes too much structure on the information. Instead, a wiki is a freeform text entry system with a fancy text-to-HTML rendering engine…nothing more. Everything else is an add-on.
From a creative perspective, a wiki allows people to express themselves in a stable environment. It frees content creators from the confines of their desktops. It eliminates existing ideas about file ownership. One person is no longer a bottleneck. Everyone can input their ideas into documents. The entire web becomes a resource to be used in your wiki.
From a collaboration perspective, document creation will never be the same again. No more “who has the latest document?” questions. No more offline conversations. No more status updates via email. Instead–all of that can happen in the wiki. Several people can edit a document at the same time 2). Notifications can be sent automatically when a document changes. And links between documents can be defined by the authors as needed.
From a structural perspective, a wiki might be viewed as total anarchy. The structure of documents is not enforced. Neither is the content. Anyone can create anything anywhere on the wiki. People are free to create their own structures. The surprising part is that people seek structure, and will strive to create it when they don't see it. There is a satisfying feeling that comes with creating something.
From a security perspective, a wiki is a highly customizable tool. A wiki can be open, protected, or private. Users can be granted rights to see certain documents and not others. Namespaces can be used to group documents for security purposes. And most importantly–users can be restricted to creating or modifying pages in only one section of the wiki. See my page on NameSpace Security for more details.