From the FAQ:
What is Burst and how do I use it?
A Burst is a powerful battle ability that randomly occurs during combat. When a Burst occurs, the words BURST will flash over one of your character portraits. If you tap the character portrait before the Burst disappears, that character will unleash a powerful Burst ability. Pay attention to battle and act quickly in order to take advantage of Bursts before they disappear. The duration that a Burst is active is affected by the speed the battle is running at, so slowing it down for more difficult battles is recommended.
Burst effects are solely dependent on the type of the Mercenary using it:
- Attacker-types deal 250 Skill Damage to one enemy.
- Defender-types gain a Provoke-like status, making them more likely to be targeted and take reduced damage. See Combat Math for additional information.
- Healer-types heal all allies by 30% of their Max HP.
- Supporter-types heal the SP of all allies by 30%.
- Special-types deal 120 Skill Damage to all enemy units.