Imagine that a man and a woman hope to meet this evening, but have a choice between two events to attend: a prize fight and a ballet.
This standard representation does not account for the additional harm that might come from not only going to different locations, but going to the wrong one as well (e.g. the man goes to the ballet while the woman goes to the prize fight, satisfying neither).
To account for this, the game would be represented in "Battle of the Sexes (2)", where in the top right box, the players each have a payoff of 1 because they at least get to attend their favored events.
Notice that once the results of the coin flip are revealed neither player has any incentives to alter their proposed actions if they believe the other will not.
The result is that perfect coordination is always achieved and, prior to the coin flip, the expected payoffs for the players are exactly equal.