The focus of the battle system is managing character classes in real time during battle.
Instead of casting cure you switch to a paradigm that has a healer and that character will do the healing. If you need haste you switch to a team that has a synergist, etc, etc.
Basically you choose the roles and let the characters do their jobs. You control one of the characters manually (think Persona 3) but since the pace of the battles is so fast you can choose auto-battle. This simplifies things because you can use several comands per turn (untill you fill all the segments of that blue bar) and selecting several attacks manually every few seconds can be too much. Some times you'll need to do things manually of course, comands like death, libra, summons and many others are never used by the AI.
It's kinda like the gambits in FFXII but without all the micro-management. In XII if you wanted to create a healer you had to create all the appropriate gambits (cast cure on a character with less than 50% hp, use phoenix down on dead character, etc). Here the AI does all the things you expect it to do within each role.
Then there's the fact that each type of attack will consume a different number of bar segments and stagger. If you manage to fill an enemy's stagger bar by chaining lots of attacks appropriately you'll have the enemy at your mercy. Some monsters are virtually invulnerable untill you stagger them, others will probably die before you even stagger them.
Not only can you stagger bosses but unlike most FF games status ailments also work on them.