In Retropolis (which is to say, in the Future we really should have had) people are pretty much like you and me. Well, like me, anyhow; I don't know you, so anything goes there, I guess. But I'll assume you were born with the usual number of arms, legs, eyes, noses, and tentacles. Okay?
So like you, and like me, Retropolitans keep their ideas in a safe place: a place where anyone, at any time, can go search out those ideas, that knowledge, or those ripping yarns that have entertained us, and experience those things for themselves. It's an archive – a literal archive – where our accumulated knowledge and stories are kept securely in a form that can be read without electricity or networks or DRM servers. A place where knowledge is free, and where it's for everyone.
This makes so much sense that I just have to pat us all on the back. That'll take me awhile, so before I go I want to point out that a Public Library is a kind of investment we make in the future, where knowledge is stored so that we'll still have it when we need it; where people stand ready to help you find the most reliable version of that knowledge, rather than the version with the most keywords; and where that knowledge will still be free, and still be readable, regardless of what else happens.