To completely beat a
video game. This term was first used for arcade games that did one of two things:
1) After reaching a certain score it would reset back to zero. For instance, a game might only be able to keep track of 9999999 points. Getting one more point after this would "flip" the score to zero.
2) After beating the last level, the game continues but on the first level. A good example of this is
Mario Bros.
This meaning of flip was
eventually expanded to include games that had formal endings.