A wiki is a website where anyone can change any webpage at any time. Think of it as a blackboard where everyone has a piece of chalk and an eraser.
Wikis usually also have a very simple markup language, or a way of formatting the text of pages. Ideally, when you edit a wiki page, it should be pretty obvious how the text you see will be displayed when you save it.
Typically, every wiki has a homepage. At the top or bottom of this page (and every page) is an "Edit" link or button. Click that link, and you'll be presented with a big text edit box, filled with the text of the page. There'll be a "Save" button at the bottom. Change what you like, and click the "Save" button. Voila, the page is changed.
On most wikis, if you smash capitalized words together LikeThis, or surround them [[with brackets]], those words immediately become a link to a page with the same name (in these examples, pages named "LikeThis" or "with brackets"). If you click on the link, it'll take you to a new, blank text box where you can fill in the contents of the new page.
What Wikis Are Made Of
Wikis are perfect for online documentation projects, where folks can get an informational page or a tutorial started, and others can fill in relevant details, fix typos, improve the grammar, and add information as time goes by.
Most wikis tend to have two different kinds of material, often called "thread mode" and "document mode." A thread-mode comment is just a comment from a participant, usually signed, like "Are you sure about this? I think the latest version doesn't do this anymore. -- Brent" Document-mode material is informational content that's not signed, like "To save your work, click the Save button on the toolbar."
Some wikis are primarily thread-mode, while some are primarily document-mode. Almost all wikis have some of both, and sometimes folks will go into a page and convert a thread-mode discussion into a document-mode block of text that summarizes the discussion.
Why Wikis Don't Fall Apart
Many, when they first hear about wikis, ask, "How can this possibly work? Why isn't each page constantly vandalized?"
Good question. First, the wiki usually keeps backups of pages. But the central reason is the Recent Changes page.
Each wiki has a page called RecentChanges or Recent Changes. This page lists every edit to every page, in chronological order, usually going back a couple of days.
But here's why that's important: if I stumble upon a neat wiki, and add a few pages, I'll be intrigued to see what's going on there. So I'll check Recent Changes. When I come back later, I'll check Recent Changes. That's the primary way to know what people are "talking" about.
If a page is vandalized--all text removed, or important information deleted, or spam added--it will show up in Recent Changes. And the people who regularly visit the site will see it and fix the change. Most wikis let anyone quickly revert a page, or immediately save the previous version over the current one.
What about contentious issues, you ask? That's really no different than a forum or chat conversation; someone has to step in and calm people down. The page may well be edited back and forth a dozen times, but eventually cooler heads prevail. Most arguments die pretty quickly, and there's usually a community prejudice against "edit wars."