In case anyone isn't acquainte with the library of Babel, it contains all possible books of a particular length (I think it's around 400 pages) which use a certain number of characters, say 30. If we assume there are, say, 2000 characters per page, we get (I think) 30 to the power of 800,000 books, a large but finite number of the sort I think Daniel Dennett called "Vast" (meaning ridiculously larger than any numbers that could be used to count anything in the observable universe. The LOB would dwarf the observable universe). It's similar to Russell's TON in that it contains essentially no information - or certainly no *useful* information. As Borges mentioned it contains the accurate catalogue of the Library (presumably occupying many lightyears of shelves, if assembled in one place) together with a "Vast" number of innaccurate catalogues. It also contains every book ever written, including the one in which the short story in question appears. This is rather similar to the multiverse, in which every story ever written is being played out somewhere (in the case of Harry Potter, with the help of an awful lot of quantum uncertainty happening to come out in just the right way).
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