A markup language is a text format adding processing instructions to plain text, usually for the purpose of either of rendering or logical organization.
A markup language might denote some semantic role of a certain string of the text, for example, document title, chapter delimiter, paragraph delimiter, etc.
Another common type of markup is presentation markup. This is the type of markup we use on this wiki. With presentation markup, you indicate what special actions should be taken during transformation of the text from raw text to the form presented to the user. Here on the wiki, we can
and more.
Typically, if one has a semantic markup, one also has some sort of means to also transform the semantical parsed text into a preferred presentation format. However, the opposite is not often true - if one only has presentation markup, it is quite hard to generate an accurate semantical tree of the document, unless the user takes great care to use presentation and content in such a way that one can somehow derive semantical meaning from the text.
These distinctions are sometimes summarized as being between procedural markup and declarative markup.