Everyday we are "burning" books by censoring them in schools or in other areas. If a book is a banned book or anything like that, we are essentially, burning the books for those that might have found use in reading it themselves. We also burn books by ignoring them and their importance in our lives.
Books and language exist as ways to pass down our culture and history from generation to generation. If we didn't have books, parts of our history would definitely be lost. I know from reading Fahrenheit 451 in the past many times (it's one of my favorites), that people begin to resist the book burning by memorizing literature and finding their own ways to pass it on. I've always thought about what I would memorize to pass on to others.