It activates the paired materia when the character is KO'd. It works with all Magic materia, all Summon materia and Command materia (Steal, Sense, Throw, Morph, Deathblow, Manipulate, Mime, Master Command only). You need to have enough MP to use the Magic/Summon, otherwise nothing will happen.

Pairing Final Attack with Phoenix is a common choice for most people.