This is the text on which a Textual Critic bases his or her own edition of a literary work. It's usually the cleanest, awesomest, most uncorrupted version of an author's work that we can find. Even this text will probably have a lot of problems, but the point is that is has fewer problems than other, messier versions of the text.
The authoritative version of a text is the best version of the text: it has the fewest problems and most closely reflects the author's intentions. Part of a Textual Critic's job is to determine which version of text is the authoritative one. Sometimes the choice is fairly easy, but sometimes there are a lot of competing texts demanding attention.
This method involves using a bunch of different versions of a literary work in order to reconstruct it in its ideal form, a version that is as close to the author's original intentions as possible.
Editing is all about fixing mistakes in texts that have been passed down to us (and fixing mistakes in texts of our time, too). Older texts in particular often have loads of printing errors, misspellings, and just outright mistakes that need to be thought through and tidied up.
A manuscript is a text written by hand. (That's not so true of literature written these days, but back in the day, that's how authors rolled.) Some manuscripts are more "authoritative" than others—that is, some are more closely linked to the author than others. Textual Critics are always searching for the most "authoritative" manuscript, if they can find a manuscript at all.
Who has authority over a literary work? Well, generally, people tend to think the author does. After all, the author is the one who actually wrote the thing. Textual Critics think we should pay attention to the author's intentions and, in the words of literary scholar Eric Cartman, respect the author's authoritah.
You can thank Textual Critic Jerome McGann for this fancy phrase. He thinks it's not just the author we need to take into account when deciding on the most "authoritative" version of a literary work: for him, editors and publishers are totally important, too. The idea is that several perspectives are at play in the production of a literary text, so focusing on just one only gives you part of the picture.
When Textual Critics can't decide which version of a literary work is more authoritative than another, they refer to it as a "fluid text." What this means is that all of the different versions of the text make up an authoritative text… at the same time.
These are things like spelling and punctuation, which Textual Critics keep an eye out for when they're trying to produce an edition of a literary work that stays as close as possible to the author's original. They may seem minor, but they can have surprisingly wide-ranging consequences.