Detailed analysis of Final Fantasy XIII's battle system from Siliconera.
"Time Gauge System Basics
Final Fantasy XIII has a brand new battle system with visible enemies. If you touch one of them the game quickly transfers into a battle where the heroes stand on one side and the enemies are on the other. Surprise the enemies by sneaking behind them and they start in "break" status. Keep that term in mind. A meter similar to the active time gauge fills up, but this meter has three bars.
You can attack when the meter is 1/3 full by selecting fight, hitting X, and then triangle. Or you can select fight three times and wait for the meter to fill up completely before hitting triangle. The advantage to waiting is your attacks link up to a three hit combo. Each linked hit bumps up the bonus gauge which determines how much damage you deal. So, lets say your base damage is 100%. A three hit combo moves the bonus meter up to around 120% which gives the last hit, sword slash or spell, a nice damage boost.
A basic fire spell takes one of the three bars to cast. Firaga takes three, but has an area of effect. Enemies and player characters move on their own, sort of like Chrono Trigger. If you launch your spell at the right time you can hit a large group, if not all of the enemies, with Firaga or Blizzaga. You can also cast Cure, but since it's in a separate menu you can't make a fight -> cure -> fire combo. You can cast Cure three times, though. Other white magic spells will probably be grouped with Cure so you can decide if you want to do an offensive combo or a recovery combo.
Lightning and Snow have also have a launch move. Remember "break" status? When an enemy is flashing activate launch as your first move and you knock them in the air. Lightning leaps into the sky and dishes out two more attacks, providing you selected fight for your next two moves, and slams them back to the ground. Any enemy in the demo, regardless of size, can be launched. Even giant ones like the Behemoth boss at the end of Snow's story.
You can launch an enemy anytime when they are in break status, but you want to launch them right away to maximize the amount of damage you do. However, if you try to launch an enemy when they aren't in break status you do around 1/8 of your fight damage. This was probably designed to prevent players from always selecting launch instead of fight."