The gauge on the right of the screen is called the bonus battle gauge. When the gauge is filled you will enter a bonus battle. Winning bonus battles result in rewards to futher boost your experience points or the amount of Fol acquired. It can also allow you to heal more HP and MP.

How the bonus battle gauge works:
» Attack enemies to charge up the gauge.
» Fill the up the gauge completely.
» Enter bonus battle mode.
» Defeat all enemies with bonus battle still activated.
» Receive bonuses.

Your battle gauge will break if:
» Your character takes a critical hit.
» Your character is killed.
» Your party escapes from battle.
» You reset the game.