Stagger is a state that characters enter under certain conditions, most commonly, when their attack has been succesfully Blocked. As expected, this only works with close-range attacks.
When a character enters Stagger, an animation is activated, in which the character is thrown off balance. During the full course of this animation, the character is completely vulnerable to attack.
Attacking a Staggering opponent also means the player will be bestowed with a higher Critical hit chance with the attack of their choice. This will only work for as long as the player can continue their combo attacks. Once the attacks have ended, the opponent can recover, the Critical hit rate will return to normal, and the battle will continue.
The ability Riposte improves the Ciritcal hit chance against a staggering opponent, making a combination of Guarding and Riposte ideal for characters such as Exdeath.
Their are several ways to make an opponent Stagger. Guarding is one option, as is EX Guard canceling, and using attacks that cause Guarding opponents to Stagger, such as Squall's Heel Crush (U.S Version).