A re-dream is an event that an individual can attempt to induce after they've been having a good dream but wake up from said dream. Many will try to re-dream the dream and think it again as they try to fall asleep. Re-dreaming is usually unsuccessful.
Bill: Man last night I was dreaming I was in a pirate war. It was really awesome but then my alarm went off!
Peter: Aw thats terrible!
Bill: Yeah, I tried to re-dream it but I was too awake for it to work.