Most basically, a wiki is a type of CMS or Content Management System. While a wiki can be used for many different purposes, many a wiki focuses on article-based content, making it an Article System.
What makes a wiki different from a traditional article-based CMS is its inherent understanding of the interconnectedness of content. A wiki provides tools to manage the relationships between different articles, in case your articles are more than just serial content.
Perhaps the most well-known feature of a wiki is its ability to let multiple users work together to write a single article. VaultWiki has this capability, but traditional authorship is also supported.
A wiki by default also keeps track of changes users make to articles, so that changes can be reversed with very little hassle if necessary.
In short, a wiki can be used for anything that a traditional article system might be used for: news, site content, blogs, etc.
The top of the page might include a header that shows important wiki information, advertisements, or other widgets.
Below that, the page is typically split between the page's body content on the left and a sidebar of various widgets on the right.
The body of a page generally has a number of tabbed controls at the top, which provide links to the editor, lists of child content, and other various options.
Then we have the page's title followed by the actual content -- what the user has come to the page to read about.
The content might be one block or several, and may end with a list of categories, feeds, and other tags that might lead the user to similar wiki entries.
Finally, the page lists the names of the users who have helped to write the content.
Some pages, if they can act as landing pages for other parts of the wiki, also include short lists of child pages to let the reader know that there is more to read inside.