Why is my mattress encased in this zippered cover and can I remove it?

Every week I have to move my Bob-O-Pedic "memory foam" mattress around and fluff it up because it gets so uncomfortable. Underneath it you can unzip all the way around the perimeter to take off this cover that it's in. I was wondering what that is there for and if it's okay to sleep without it there? The mattress seems like it'd be softer without it.