Finisher does one of three things:
1.) Guaranteed Critical Hit,
2.) Elemental strike, corresponding to the character's element (Bartz = Wind, Lenna = Water, Krile = Earth, and Faris = Fire), and I've yet to see this do anything other than 9999 (Unless the enemy's elemental defence nullifies it. I mean...it is an elemental strike)
3.) Nothing. Nada, Zip, Zero, Zilch.