As you might guess from the title, the theme of religion pops up a lot in "The Secret Miracle" –but not always in the way you might expect from a story about a Jewish writer. The story opens with an epigraph from the Qur'ān, the holy book of Islam, and the protagonist searches for God in a Catholic library. While Borges makes plenty of references to Jewish culture and literary tradition, Jaromir's prayers and interaction with God don't seem particularly Jewish. Instead, his spirituality seems like it could belong to any of the three big monotheistic traditions that have grown out of the Hebrew Bible. This makes sense: after all, Borges doesn't care much about the ways in which religions exclude one another, but rather about the ways in which they can relate to one another. He and Bono would have gotten along swimmingly.
By referencing Islam, Judaism, and Christianity, Borges makes Jaromir's story seem universal: his experience isn't just a Jewish religious experience, but a human one.
People tend to think of this story as a work of "magical realism," a genre that combines plain old ordinary events with crazy supernatural stuff. In this case, though, the supernatural event is an act of God, so we should call it "divine realism" or "spiritual realism."