Triple Attack is an enemy ability used by Fafnir. Triple Attack itself is almost identical to Fafnir's normal attack, the only differences are that it has quick hit properties, and it cannot break the damage limit. However, in the same turn, it is immediately followed with an elemental breath attack, and then another physical attack, thus the name Triple Attack is most likely referring to the three-attack combo as a whole.
Triple Attack is a Thief-only Job Trait in Final Fantasy XI. It is available only to high-level Thieves, starting at level 55. The exact formula that determines when this is activated is still a mystery. The ability itself is very much like Double Attack, though. Every once in a while, instead of attacking once, the player with this ability will attack three times. The Triple Dagger and Assassin's Poulaines enhances this ability.