"The Library of Babel" explores the fine line between the material act of writing and the meaning of language. We tend to take it for granted that most things that are written down are legible, but in the case of the Library, most of what is written down is totally incomprehensible to its inhabitants. In one giant thought experiment, Borges takes us through all of the implications of living in a world where writing exists for its own sake, and people have to try to interpret it with human inventions like languages and codes. In the end, Borges blows our mind by showing us how language itself unravels in the face of the eternal Library. Can we even be sure we understand the very story we're reading?
Writing is completely meaningless in this story. Any meaning it may have is projected onto it by the human inhabitants of the Library.