Libraries are a favorite symbol for Borges, who spent some of his most creative years writing stories in the basement of a municipal library. Sound fun? Well it gets even better. Toward the end of his career (years after publishing "The Secret Miracle"), Borges went blind. Oh, and he was the Director of the Argentine National Library. So it's pretty convenient that one of the characters in this dream is a blind librarian.
The library that appears in "The Secret Miracle" is the Clementinum Library (a.k.a. the Klementinum Library), which was founded by the Jesuits (a congregation of the Catholic Church) after they arrived in Bohemia in 1556. Given the metaphysical nature of Jaromir's quest – in his dream, he's searching for God – the religious association of the collection is definitely significant.
Also, check this out: the fact that it's a Catholic library means that all of the major monotheistic religions – Islam, Judaism, and Christianity – are mentioned in this story. Way to be universal, Borges. As always.
Like all of Borges' libraries (especially his famous "Library of Babel"), this one is a treasure trove of information, but not a very organized one. In fact, people in the library suffer from information overload, and can't seem to find what they're looking for. The blind librarian tells Jaromir that he's gone blind searching through the library's four hundred thousand tomes, and that his parents and grandparents didn't have much luck, either. The fact that Jaromir succeeds in finding the divine letter is pure luck – or, dare we say, fate.