Meta is a term you’ve probably come across in jargon such as “metadata”. You’ll hear it quite often in relation to media and fandom. Meta refers to the self-referential nature of something.
For example, a metafiction might be the “play within a play” featured in Hamlet. It might be about a character who knows they are in fictional universe. It might a story about a storyteller, or a movie about filmmaking. It might invoke the conventions of narrative such as in the Discworld novels by Terry Pratchett in which “one-in-a-million chances crop up nine times out of ten”, because, as the characters themselves understand, that is how stories work.
Meta is often used as a blanket term within fandom to denote critical analysis and discussions about media artefacts. This is not the same as a review such as “The cinematography is good but the plot is poor”. Instead you will find readings such as “Sherlock’s Coat: The Importance of Costumes” focussing on the BBC’s Sherlock or “Comparing BBC’s Sherlock to Arthur Conan Doyle’s Holmes: Misogyny and Subtextal Homoeroticism” or “Reading Ron Weasley as Bisexual” or “Magic: Representations of Wicca and Neo-Paganism in Popular Media”.
These types of readings are common in academia, where, for example, feminist readings or Marxist readings of a text are used to critically examine a book, film, or television series. Fandom however has picked up on the tools used professionally and uses them to start their own discussions about subjects of interest.
Meta in this sense can also denote metafiction as discussed above, such as a map of Hogwarts (Harry Potter), or works intended to assist fans to create other fanworks such as a character list giving key facts as a ready reference, or a primer on writing about emergency medical treatments to give realism to fanfiction.
In fannish terms then “meta” can refer to a variety of non-fiction texts as well as texts incorporating the self-referential nature of storytelling. For many, it’s an interesting and important part of fandom. Fandom is about more than just reading a book or watching a film or show or listening to a particular band. It’s about a sense of community with other fans, but it is also about engaging with the work which can include discussing it, analysing it, and creating transformative works inspired by the original work.
Meta is about taking a deeper look at a work, comparing and contrasting, reading it from different angles. It recognises that media is important, that it informs us and our world, and as such, deserves to be studied as well as enjoyed.
The Wikipedia Metafiction page has more examples of the types of metafiction while the TV Tropes Million To One Chance page gives examples of that trope, including that of the Pratchett usage mentioned here.
None of the fandom specific meta titles given here are real but were created to give a feel for the types of meta created. It is considered poor etiquette to link to specific fannish endeavours outside of fandom without prior permission. However searching for “meta” and your favourite fandom will probably bring up some results if you’re interested in reading some examples, though as with all work, professional or fan-created, quality varies considerably.