Dust Jackets

Could someone please explain to me why books have dust jackets? Are they, as the name implies, to keep dust off of the books? Or to make books look pretty?

I just don’t know what to do with the dust jackets. If I leave them on, they get torn and I feel badly, but now I have a stash of dust jackets and I have no idea what to do with them. Should I keep them? I am very clutter-phobic, so the thought of a big pile of paper that I will never use gives me chills. I know we have some librarians who comment regularly. Clearly, this is not the most substantial question asked on this blog, but thoughts?