Oyose means large yose.
Large yose may be played early in the game. However, many games reach a point where groups are fairly well settled and the board divides itself into independent or nearly independent regions, but the remaining plays are still large. Such a stage of the game may be called the oyose stage, large yose stage, early endgame, or macroendgame. Stage may be left out. Hence, the phrase, "The game entered the oyose."