The original version of Final Fantasy XIV didn't have any of the typical Final Fantasy jobs. Well, it didn't have any of the typical job names, anyway. For some reason they'd decided to switch all the names up for the races and the classes. Instead of being a Mithran Black Mage you'd be a Mi'qote Thaumaturge. It was one of the many things they did that may have had a good reason, but that the players universally hated. It turns out one of the things a Final Fantasy game has going for it is all the history from the earlier games and throwing that away for no reason makes people unhappy.
Ultimately they decided to fix that problem by adding a job system on top of the class system. I don't know how it worked in the first version but I looked into how it works now and it's pretty straightforward. There are 8 quests you can do to unlock the different jobs (each of the 7 classes has one, and Arcanist has two) and the jobs share experience with the associated class. So my level 33 Arcanist actually means I already have a level 33 Scholar and a level 33 Summoner. Or I will if I go do those two job quests. In order to do the quest I need to be level 30 of the main class (Arcanist in these cases, which I have) and level 15 in a secondary class. Which will be Thaumaturge for Summoner and Conjurer for Scholar. I don't have those, but 15 is pretty low so picking those up should be pretty quick I think.
What does switching to a job do for you? Well, you keep all your old abilities from the base class and you get some extra ones that specialize you more in one direction or another. You also have your multiclass abilities restricted down to being from only 2 classes instead of from all the classes and you only get half as many. So it seems like you get better at doing one thing but lose a bunch of versatility, but that's generally a fine trade in an MMO. Especially for dungeons, and especially for an Arcanist since Scholar is a healer job. And any experience gained while playing as a special job gets assigned to the base class.
All this means I have more stuff to go do! I especially want to get the Summoner class so I can bust out more than a Carbuncle pet. From the ability list it sounds like I can go beat down with Ifrit! Woo! So I need to go level Thaumaturge up to 15 and then do the quest chain. But first I want to get to 35 and unlock the levequests for miner... So much to do, so little time...