Bonus Play is an unlockable feature in the God of War series, made available after beating one of the diffculty modes in the game once.
In God of War: Chains of Olympus
There's also a similar feature in God of War: Chains of Olympus. It works the exact same way it does in God of War II.
In God of War II
Bonus Play was first implemented in God of War II, this extra game mode allows you to replay the game on the same difficulty it has been beaten before, however, the player retains all of their magic powers and health, and is automatically equipped with all the subweapons, including the Blade of Olympus, Bonus Costumes can be selected before beginning the bonus play mode, and any or all Urns of Power that have been unlocked in normal play can be activated during this mode.
In God of War III
During Bonus Play, your health, magic, and item gauges are at the same level they were when the game was finished.
The Bonus Costumes can be used as well, and any or all Godly Possessions that may have already been unlocked.
However, using other costumes, or godly possessions, disables trophies.