Wiki markup is a kind of markup language, like HTML, that is designed to be pretty easy to learn and use. There are several different kinds of wiki markup (think of them as "dialects" or even different languages); the pdx.wiki.org uses Mediawiki software and markup.
What is a markup language?
A markup language is a syntax that makes it possible to use plain text to make fancy things (like formatting, hyperlinks, displaying images and forms, etc.) happen when it's displayed.
Back in the stone ages of computers (like 10-20 years ago), word processors like WordPerfect allowed "power users" to directly edit the code -- or the markup -- if the expected document didn't look the way it should. In modern word processors, the markup is generally not visible, but it's still there "under the hood."
When creating web pages, though, it's often essential to edit HTML markup code to get the desired result. The idea of wiki software is to use a simpler, more human-readable markup system than HTML; it's still usually necessary to deal with markup, but the markup is much nicer to deal with than HTML.