Once the indicated skill is unlocked it will give the corresponding bonus.

Anti-grav Jump: Hold Jump to travel further.
Bargain Hunter: Purchase items from shops at 25% discount, also affects Serendipity coin prices.
Battlemania: Increase the odds that rare enemies will be encountered.
Chocobo Music: Select Chocobo songs while riding the Chocobo.
Clock Master: Set overall game speed between High Speed and Low Speed.
Encounter Master: Change the enemy encounter rate to frequent or less frequent.
Eyes of the Goddess: Control camera in Event Scenes with Right Analog-stick.
Field Killer: Defeat enemies instantly on the field.
Haggler: Sell items to shops for 10% more gil.
Mobile Mog: Lets Mog return to your side faster after throwing him.
Mog's Manifestation: Improved Moogle Throw to find always treasure where none can be seen.
Monster Collector: Increase odds to obtain a Monster Crystal from battles.
Paradox Scope: Invoke paradox to explore new potential histories to challenge history's new possibilities.
Rolling in CP: Earn more CP from battles.