Books represent knowledge and awareness. Like the forbidden fruit in the futuristic Eden that is Montag's society, books are forbidden by the state in its hubris. Books are referred to metaphorically and in simile as birds, their pages wings. Transversely, it seems, they represent freedom that knowledge brings and that freedom's ability to transcend - to fly. The significance of fire is also manifold.
Fire represents purification as it is used to rid society of that which is undesirable.
Books and the places where they are hidden are eradicated by fire - they are burned out of existence so as not to contaminate society, just as dirt is washed from one's hands. Captain Beatty mentions the standard practice of immediately cremating the dead so as not to be burdened with decaying bodies and memorials and the grief associated with them. Fire also represents awareness. It smolders for days. Well, this fire'll last me the rest of my life.