Yeah, you read that right. In the Library of Babel, words themselves are symbols. "Hold up a second," you might say. "Don't we use words to communicate? Aren't words supposed to have meaning?"
Well, yes, but Borges makes the point that words don't have inherent meaning. That is to say, a word doesn't mean something because the universe has divinely ordained it to be so. There's no dictator of language who tells us the word "dog" means "a fuzzy, friendly creature whose poop you have to scoop." No – words have meaning because we give them meaning. And that meaning is sort of arbitrary. It can differ across cultures, languages, and time periods. It can even differ between individuals. There's no real clear way to know that the word you say will be completely and clearly understood in the way that you intended by the person you say it to. Borges makes that point when his narrator asks: "You who read me – are you certain you understand my language?" (13).
Words are symbols in this story in the most basic way possible: they are signs that stand for something else. This is the basic premise of an idea in linguistics called structuralism, thought up in the early 20th century by a guy named Ferdinand de Saussure. Saussure's ideas about the arbitrariness of language went on to influence an entire generation of writers and literary critics.