Okay, so the setting is kind of a big deal in this story. It's in the title (see "What's Up With the Title?"), the first line, and the first several paragraphs. The Library works as a symbol (see "Symbolism, Imagery, Allegory"), but it also structures nearly every other element of the story. It pretty much informs all of the story's themes, the characterization of the solitary character, and what little plot there is (see "Classic Plot Analysis"). It even affects the writing style.
Like we said, the fact that this story takes place in a library – The Library – is a big freaking deal.
Here's why: this story is all about language. The Library turns out to be a model of the universe in which the idea of language is tightly controlled. Because the Library is really, really structured, it's the perfect playground for Borges to toss around a few ideas. It's like a little science lab where language is the experiment. In the Library, we can think about language in a really abstract way, because it's not hampered by all of the messy details that confuse issues in the real world, like culture, nationalism, and passion. In the Library, messy human inventions like religion are trivialized. The real focus there is language.