The more you use a special art or spell, the more potent it becomes. You'll know how many times a special art or spell is used by access the Special Arts/Spells menu and selecting a spell or art. Look for the "Used" counter in the spell/s.art's description window.
Aside from the visual changes in the spell or art's animation when used, you'll also noticed increased damage, faster casting time, and additional hits for multi-hit Skills. When you find a good special art or spell, keep using it frequently to increase the character's proficiency with it.