A Wiki is a website that allows any authorized user to collaborate with other users in the creation and editing of a web page.  The most well known wiki is Wikipedia combining the technology of a Wiki with the idea of an encyclopedia.  Using certain kinds of Wiki software, Wikis can serve any personal, collaborative, or company interest.  They can be created for specific things like Google Sites, a company's intranet using Microsoft Sharepoint or a personal wiki using Tiddlywiki. 

History

Ward Cunningham created the first Wiki in 1994, it was called the WikiWikiWeb based off a bus in Hawaii, that the word Wiki Wiki meant quick.  The WikiWikiWeb was implemented between 1994 and 1995, and the official start day was March 25, 1995.  It was started to aid the Portland Pattern Repository which designed patterns.  Programmers could then collaborate on ideas to create computer programs, not design quilts.  The beginning of the WikiWikiWeb worked a little like a bulletin board, where when users posted information, it would push down the older information.  Eventually he edited the site to work like how Wikipedia does now, which garnered more popularity.

As of today, the original Wiki site is still running here, there is more history on the page including statistics and other information.

Types of Wiki Software

Semantic - A wiki that has information tied to the information. For example, the word apple would have the tag fruit, colors associated with apples and possible uses. This information can be queried if a person wanted to find fruits of a certain color and the such.
Enterprise - A wiki used for corporate companies where there is more control over the site than normal. A company may fuse this within their intranet to allow employees to edit information such as updating the site with news about the company Since these types of Wikis are controlled by the company and there is no internet anonymity, the information is usually correct.
Application - A wiki that allows users to do programming inside of the wiki.  Compared to an Access database where normally users are just allowed to enter in information into forms, an application wiki allows users to edit those tables and forms.
Personal - A wiki that isn't meant to be shared with others.  There may be little collaboration if the user decides to share the wiki with a few select people.
Mobile - A wiki optimized for cell phones.  Usually these types of wikis decrease the size of the page by taking away images, color, and making the text plain allowing a cell phone to load the page faster.

Users of Wikis

For open wikis such as Wikipedia, anybody with an internet connection can edit any information on there.  Generally, the information is usually accurate, but there comes the one time a person feels like being not such a nice person and wildly goes about editing/deleting information.  Most public Wikis like Wikipedia have you register to be a user or it logs your IP address for any changes you made.  If either kind of user tampers with the site, the account or IP address may be banned not allowing any future changes.  By being a registered user, many sites offer additional benefits in the form of more tools to modify the site.

Even by being a registered user or logging IP addresses, people are always looking to do harm.  For very open sites such as Wikipedia, there are very high chances that information may become messed up.  Fortunately, editing histories are saved, a little similar to Google cache, the older version of the page is saved and is reverted back to in case someone goes rampant.  But for sites such as Citizendium, it's a very tight knit community.  Citizendium requires its users to use their personal information so every user knows every other user, and if a change is made, it's known who does it.

Editing of Wikis

Wikis generally use Wikitext to edit their webpages.  Wikitext is a simplified language where users are able to easily edit information without going into the mumbo jumbo of HTML.  With HTML, users may get confused with all the tags to edit the information, and it may become hard to read.  With Wikitext, simple keys are used to do things.  Some wikis allow both Wikitext and HTML to further customize the site, but often don't go past HTML.  Keeping Wikis to Wikitext and HTML keeps sites helps keep a consistent layout.

A very important concept when it comes to the editing of Wikis is WYSIWYG, or What You See Is What You Get.  As Wiki technology becomes more advanced, it becomes more user friendly.  The concept of WYSIWYG is unlike Wikitext and HTML, what you see and edit on the edit screen is almost exactly like what you see on the final product.  WYSIWYG is usually powered by JavaScript or Active X controls, both of which are never seen by the public and are already implemented into the system.  Google Sitess is an example of WYSIWYG, as we type out what we want our sites to say and then click save, it looks very similar to the editing page.

Criticism

There's much criticism about the accuracy of a wiki especially when it comes school, because since almost anybody can edit the information, fiction may become fact.  In most cases, this can be alleviated by placing a reliable source of where the information was taken from.  If the information is untrue or source deemed unreliable, the web administrator or another user may edit the information out.

References

http://en.wikipedia.org/wiki/Wiki
http://en.wikipedia.org/wiki/Wiki_software