What does "very meta" mean?
"Meta" is being used in a rather informal, somewhat regional sense there. The OED does, however, have an entry for "meta" (adjective) in the applicable sense.
Have you ever heard of a "meta-analysis"? In the academic world, it is an analysis of analyses, or a study of studies.
In TESOL, we often talk about the need to minimize the use of "meta-language" -- i.e., grammatical terminology, language about language -- in our explanations.
In your quote, something similar is happening. They own a bar, and they've named it The Bar (cf. a Japanes restaurant called Japanese Restaurant).
A: Have you been to The Bar?
B: I don't think so. What is The Bar?
A: It's a bar.
A: Have you been to Japanese Restaurant?
B: I don't think so. What is Japanese Restaurant?
A: It's a Japanese restaurant.
Here is the applicable definition from the OED (The Oxford English Dictionary):
2. orig. and chiefly U.S. Frequently in predicative use. Designating or characterized by a consciously sophisticated, self-referential, and often self-parodying style, whereby something (as a situation, person, etc.) reflects or represents the very characteristics it alludes to or depicts.
1988 5 Sept. 17/2 He predicts that, like ‘retro’..‘meta’ could become independent from other words, as in ‘Wow, this sentence is so meta’. If so, you heard it from me first.
1993 8 Aug. (Electronic ed.) When anchorwoman Connie Chung made a guest appearance on sitcom Murphy Brown to advise anchorwoman Murphy not to sacrifice her journalistic integrity by making a guest appearance on a sitcom, that was just plain meta.
1994 D. Rushkoff iii. x. 127 Everything relates to house in a self-conscious or ‘meta’ way.
1999 Aug. 58/1 An enterprise such as Brill's Content is inherently ‘meta’, since it doesn't review movies, for example, it reviews the reviewers who review movies.