The three main class categories in the Elderscrolls games represent, sort of, social classes, which mimic the major social classes of ancient societies.
The mage class is the upper class, which, in ancient times was usually the priestly class, or some ruler who had the blood of a God in his veins. They also, especially the priests, usually guarded or pretended to guard some ancient knowledge that they refused to share.
Likewise, there are pockets of powerful mages throughout Tamriel, like the Telvanni and the Psijic Order, who possess secret knowledge they refuse to share. And, in general, the mages represent the scholarly class in Tamriel.
The warrior class is, of course, the warrior class. They are honored and pretty well-off, but NOT nobles. They worship their own, more barbaric Gods and live in less lavish abodes, generally all in the same, big abode. Like Cloud Ruler Temple in Oblivion, or any ancient Roman legion fort. And of course, the noble who fights alongside the warriors, and leads them into battle is the most honored and respected in any ancient society, just like the battle mage is the most powerful class in Arena, and in future games, if done right.
Then, the thief class is the lower class. The factions these characters join are generally the underground factions.
Kind of makes sense.