Freelancer - The default job! In other words, Bartz is in Freelancer mode most of the time. In the game, the Freelancer has all the innate abilities of any mastered job and can use any job's learned abilities.
To be fair, the Freelancer can't use all of the high level abilities for a job that hasn't been leveled enough. So while White Mage can use a high level spell like Holy; if the job isn't leveled enough, Freelancer can't use it. If a job is mastered, it's at its max level.
This list is mostly here because for the sake of consistency and because I'm a hopeless dork. Otherwise, I honestly can't think of a time when Mystic Knight would come in handy.
Knight - A job that wears armor and equips a shield and a sword. Can also Cover people by taking hits for them.
***Mastered!
Monk - A job that fights with his feet or fists.
Thief - A job that specializes in agility and thievery. Uses daggers and knives.
Black Mage - A job that uses offensive magic. He can cast spells like Fire, Blizzard, Thunder. He can also use higher level stuff like Bio and Flare.
White Mage - A job that's all about healing. He can heal with spells like Cure, Cura, etc. or cure status ailments.
Blue Mage - A job that can use skills learned from monsters. So far he's got... Goblin Punch. Hooray.
***Mastered!
Red Mage - A job that can use low level black and white magic as well as cast spells twice in succession! Too bad he never mastered this class, so no double cast for Bartz!
Time Mage - A job that has control over time and space. They can speed up things with Haste, slow down things with Slow, and even cast high level spells like Comet and Meteor.
Summoner - A job that can summon monsters to attack for them. Examples include Ifrit, Shiva, and Ramuh.
Berserker - A job that is completely useless specializes in attacking powerfully by being in the Berserk status at all times. Uses axes.
***Mastered!
Mystic Knight - A job that has the ability to imbue weapons with elemental power.
***Mastered!
Beastmaster - A job that can control and capture monsters. Uses whips.
Geomancer - A job that uses the terrain as a means of attack.
***Mastered!
Ninja - Best job ever A job that's... a ninja. What more is there to say? This job can wield two weapons at once, throw shurikens, other weapons, magical items, and so on.
Ranger - A job that uses a bow and calls upon the power of forest animals for help. Uses bows and arrows.
***Mastered!
Bard - A job that uses magical songs to attack enemies or help allies. Uses harps.
Dragoon - A job that uses a lance and can attack enemies by jumping high into the air.
Dancer - A job that uses magical dances to attack the enemy or help allies.
***Mastered!
Samurai - A job that wears heavy armor and uses katanas. Is also capable of hurting enemies by tossing money (I don't really get it either) and drawing his weapon really fast.
Chemist - A job that mixes two potions together to make... better potions.
***Mastered!
Mime - A job that can mimic the actions of others.