Wikis are sites allowing users to add and modify content. Wikipedia is the most popular (using the MediaWiki software which is open-source and also used on many other wikis), but there are many others. While an increasing number of wikis use rich-text editors now, wikis traditionally used some form of wiki markup for editing purposes, which was intended to be simpler for novices than HTML, but over time tended to get complicated as features such as tables and templates were added.
"Wiki" got its name from a native Hawaiian word for "quick".
There are loads of types of Wiki markups associated with different software (and different versions of the software), though there are some traditions, including the use of square brackets (single or double) to enclose hyperlinks. (However, some wiki markup, though not that of MediaWiki, automatically hyperlinks anything typed in CamelCase, with capital letters in the middle of a word.)
Markdown is a similar sort of simplified markup language.