Definitions for halftime
Random House Webster's College Dictionary
the intermission or rest period between the two halves of a football, basketball, or other game.
(adj.)pertaining to or taking place during a halftime.
Origin of halftime:
an intermission between the first and second half of a game
The halftime show, the primary "light" entertainment of a game, after the second quarter when players can physically recover, coaches can berate players with a pep talk, bets can be doubled, etc.