A Support Job, also known by its abbreviation subjob, is a secondary ability skillset that appears in several games.
Characters start with a main job. Upon reaching level 18 they can do a quest in either Mhaura or Selbina to gain access to a Support Job. A support job is a sort of secondary specialization. When a character has a support job, they gain additional HP and/or MP, statistics as they level up, spells, and/or abilities.
A character can level up any or all 20 basic and advanced jobs. Each of these jobs starts at level 1 and must be leveled independently, which is different from what people might have been used to in Final Fantasy Tactics.
A character who has completed the Support Job quest can level with a support job. This is generally displayed 1WAR/1MNK (Warrior/Monk), in this case standing for first level Warrior, the player's main job in which he will gain experience, and first level Monk, which is the character's subjob. The player will gain all abilities and statistic boosts that apply to their support job, but the support job will not gain any Experience as the player progresses.
A support job is always considered, at maximum, half of the level of the player's main job. In this way, a level 10 Warrior who wants a support job of Monk would be at best 10WAR/5MNK. In order to do this, the player must have at least leveled their Monk to level 5. A 10WAR/5MNK will thus have all of the job abilities and traits of a level 10 Warrior as well as that of a level 5 Monk.
In the case above, Warrior/Monk was used as an example. A player can choose any combination of main job and support job. With 20 different jobs, that means there is a possibility of 380 different job combinations. That said, the majority of these combinations are nonsensical for most situations in the game.
Mages, for instance, will probably always choose another MP-based job, usually Black Mage or White Mage. Fighters will almost always choose another melee job, usually Warrior, Ninja, or Thief. Tanks will almost always choose Warrior for its Provoke job ability.