Gag reels have been around Hollywood for a long time. They certainly predate DVD and LD supplements.
Traditionally, the editor (in cooperation with the director) will put together some of the funnier outtakes/mistakes/etc. captured while filming a movie and cut them together. This reel is traditionally shown at the wrap party for the film. (a party for the cast and crew at the end of principle photography)
They often contain bloopers, in-jokes and shots of the cast and crew hamming it up. It is for this reason that gag reels as seen at movie wrap partys are usually not shown in the supplement section of a DVD. (I'm sure certain Hollywood stars would object to some of the outtakes being shown to the public) Plus, some of the material may not translate outside those who worked on the film (i.e. there may be a shot of someone who worked in wardrobe spliced together with someone in transportation - because everyone knows they were having an affair on set etc.)
They are often temporary things spliced together and, with a few notable exceptions, never seen by anyone outside the immediate cast and crew. They usually run 10 minutes or less.