Wikitext language, or wiki markup, is a lightweight markup language used to write pages in wiki websites, such as Wikipedia, and is a simplified alternative/intermediate to HTML. (A lightweight markup language is a markup language with a simple syntax, designed to be easy to enter with a simple text editor, and easy to read in its raw form.) Its ultimate purpose is to be converted by wiki software into HTML, which in turn is served to web browsers.
From MediaWiki.org:
Wikitext is a document written in a wiki markup language, such as the current one explained in Help:Editing (see also Markup spec/DTD). It is a mixture of content, markup, and metadata. The current and old versions of all pages of a wiki are stored in the database in the text table, in the form of wikitext.