What exactly are these meta text/tags?

In simple terms, meta tags are specific codes that include snippets of real text such as a paragraph or a list. Each page in a web site can have meta tags containing text that is unique to that page. There are lots of variations but the two most useful types of meta tags are the 'Description' and 'Keywords'.

Description contains a sentence of up to 150 characters that describes the page content.

For example: The Twice as Loud theatre company present news of their performances at fringe theatre venues in London and monthly new play reading evenings.

Keywords contains a list of, ideally, around 25 words selected from the visible text.