Compiling that much data over what would likely be a very long term would require research into novel storage technologies. Concerns about media format, translation, and data compression would be confronted, along with seemingly intractable issue of copyright. Most importantly, the Off-Site Backup Project would allow human civilization to rebuild after the unthinkable happens. It's widely accepted that an asteroid strike killed off the most successful biological family in Earth's history, the dinosaur. As with the asteroid that killed the dinosaurs, it is highly unlikely that a global disaster would wipe out every living thing.
Human beings are particularly resilient.
Those people that would remain, however, would struggle to rebuild, and much of what humankind had learned would be lost. The off-site backup would keep human knowledge intact, available in such an emergency. Our Moon is a good candidate for a first attempt at such a backup. It would be a good test site, to make sure the system works. A living, growing human colony alongside a storehouse of civilization's knowledge, would make it nearly impossible for a disaster to wipe out all of humanity.