Trance
What basically replaces the Limit Breaks from the previous Final Fantasies is the Trance feature. It basically allows any character to increase their strength and be able to do their skills stronger and with ease. For most characters, the trance command doesn't really effect add any new skills. It actually resembles more of a Berserk status change than to the previous Limit Breaks of Final Fantasies prior. The Trance gauge fills up in a unique way. It increases when you take damage from enemies and it decreases when you attack. It automatically goes to zero at the end of a battle, and it's physically unviewable. Trance is more connected to the emotions of character in battle, so it makes sense that it functions in this sort of way.
Zidane - Dyne : The Skill command is replaced with Dyne. It basically is a set of abilities that Zidane learns that become super-powered when you goes into Trance. Dyne uses low MP to execute the skills and Zidane basically becomes stronger.
Vivi - Double Black Magic : Black Magic is replaced with the command Double Black Magic. He gets the ability to cast the same Black Magic spell twice, however it costs the same amount of MP as it would casting them seperately.
Garnet - Eidolon : Summon turns into Eidolon on the command menu. Basically its the same thing.
Steiner - Double Sword : Steiner's strength is doubled for everything, Sword Art and Magic are still there.
Freya - Jump : Freya Jumps Into Air, and Deals Damage There.
Eiko - Double White Magic : White Magic is replaced with the command Double White Magic. She gets the ability to cast the same White Magic spell twice, however it costs the same amount of MP as it would casting them seperately.
Amarant - Flair : His flair abilities can strike more.
Quina - Cook : Eat is replaced with Cook, makes it easier to eat enemies.