What about class levels? Since a wizard has to prepare his spells ahead of time, he knows exactly how much he can do at any given time, and no amount of willpower or effort will allow him to do any more. And then, one day, he wakes up in the morning and says, 'Hey, I can prepare several more spells today than I could yesterday!' And when wizards sit down and take notes, it'll turn out that, in fact, all of them have experienced the same phenomenon. How can they not come to the conclusion that there is some stratified system for magic, where a person has a measurable rank?
Of course, fighter types are not terribly likely to go around, say, conducting statistical tests on how often they can hit each other, and common folk tend to have no clue what is going on. But people need a language for describing things; even Joe Sixpints at the tavern can tell (barring magical misdirections) that Timron, the King's Magician, is someone to be more afraid of than Bumplekin the apprentice, and he needs a way to express that clearly. So why not tie it to level, in an indirect way?
In my campaign, just about everyone describes other people in a numerical way... but, everyone's level is more or less a subjective thing. For a real-world analogy, consider sitting around at a bar with your friends, rating the attractiveness of other patrons. "Wow, there goes a perfect ten!" "Are you kidding? I'd say seven at best." Um. Not that I ever do that. Just looking for a common frame of reference. As for the classes themselves, people use all kinds of colloquiallisms. People who fight in melee are generally called 'blades' (or 'fists' for monks), while ranged attackers are 'slings' and 'arrows'. Rogues, depending on reputation, are either 'coins' or 'shivs', while bards are usually 'strings' or 'songs'. Casters in general are called 'scrolls'; people who know enough to know the difference between arcane and divine casting may have more specific terms for them ('books' for wizard, 'bloods' for sorceror, 'signs' for clerics). Traveling to different regions may change any or all of these terms.
As I said, all of this is based on subjective opinions. When a lush at the tavern tells you, "I wouldn't go messing with old Bodazian; he's eleven books if he's a single cantrip!", he doesn't literally mean that Bodazian is exactly an 11th-level wizard. Bodazian could be a sorceror, or even a divine caster (depending on how well-informed, and how drunk, the guy is), and he could be just about any level. It's just one man's opinion. Similarly, a 5th-level rogue could go around claiming to be 'a warrior of nine blades', and unless you want to challenge him to a trial by combat, you'll just have to believe or disbelieve him as you see fit.
