Since Magic was initially created there have been effects that grant players extra turns. For example; Time Walk, Time Warp, and Final Fortune. In the vast majority of cases how to deal with these extra turns is simple and obvious. If a player generates an extra turn, they will just take another turn after the current one it over.
However it is possible for different players to use different effects to generate multiple turns. If two different effects are trying to give different players an additional turn, which wins? In Magic, the most recently generated extra turn will be taken first. While taking turns does not use the stack, it may be useful to think of turns as if they did. Like spells and abilities on the stack, the top most one resolves and happens first. Normally in a two player game, the ‘turn stack’ simply alternates between the two players. When someone generates an extra turn, this turn goes on top of the stack, it will disrupt to normal pattern and this turn will be taken next. So if two different players generate extra turns, the last effect to resolve and create an extra turn will ‘win’ and be taken first. Then the additional turn that was generated first will be taken. Once that turn is over the game will return to its normal pattern.