The job system is a layer over the existing Armory class system and is actually a series of gemstones that you equip while on specific classes. The jobs themselves don't have levels, they simply become the level of the main class that supports it. Paladin is based off Gladiator, Black Mage off Thaumaturge etc. XP gained while equipped with a job stone goes toward progression of said main class.
The cool thing with jobs is that their ability progression (along with their AF) is quest based. The quests themselves have a main class level requirement. Which basically means you don't have to level a whole other class. When the patch hit, I was level 50 Lancer. Since I also had level 30 Pugilist, I met the requirements for the Dragoon job quest (30LNC/15PUG) and was able to get that job stone. Once you receive the job you get one signature job-specific ability that cannot be used with any other class or job. For Dragoon, you get Jump. You get follow-up quests to that storyline every 5 levels - 35, 40, 45 and 50 respectively. Each quest rewards you with a new job specific ability/weaponskill. When you reach level 45, you begin picking up your AF as parts of the 45 and 50 quests.
One thing to know about jobs is that in many cases they are superior to classes with two very very important exceptions.
1) It limits you to the abilities of the two prerequisite classes for the job.
2) The number of ability slots you have is cut in half.
While this may not seem too bad, there's some instances where you miss out on some really key skills when you go on a job vs on a class. PLD for example has zero access to useful skills like Invigorate (TP over time), Second Wind (45 second free heal - TP cost removed this patch) and Featherfoot (Dodge that returns a small amount of MP). Instead you're locked to Conjurer and Gladiator abilites only - which with the revamp to skills from 1.19 - it basically gives you Cure and Protect as your only useful CON skills. So right now, PLDs either need to travel with a pocket BRD or bring stacks of high ethers.
Some jobs, like WAR, MNK and DRG completely destroy their corresponding classes. DRG gives up some survivability for an insane boost in damage, MNKs are crazy DD with very little lost, and WAR... well, WAR is the best tank in the game right now - stupidly high damage, plate armor and almost 50% more HP than PLD with non-MP heals (not as self sufficient as PLD, but when you're hitting like a freight train, battles of attrition are rare.)