Historical Rules · 25 September 2014
Rule 715.1a
Official source text from the 25 September 2014 Rules release
A “subgame” is a completely separate Magic game created by an effect. Essentially, it’s a game within a game. The “main game” is the game in which the spell or ability that created the subgame was cast or activated. The main game is temporarily discontinued while the subgame is in progress. It resumes when the subgame ends.