It is a phrase that was used by video
rental employees after handing customers their video tape.
The act of rewinding a video tape after
watching it is considered a kind deed, as the next person to watch that tape wont have to
rewind the entire movie, which might spoil the storyline for them if they watched the screen while it rewinded.
Video guy: "Here is your tape bro!
Be kind rewind."
Customer: "Thanks man. I'll make sure my parents aren't home when I'm
watching it."