I don't think we can really say much about XP as it stands now, since I think each time someone came up with a class, they had an entirely different model for what XP actually meant. But if we restrict ourselves to just the three classes in the original books, and focus more on the fighter vs. magic-user relationship, I think a good case can be made for the experience point requirements as a reflection of how respectable each class is in the eyes of the general populace.
Start first with how XPs are earned: killing monsters, returning to town with treasure. This doesn't seem realistic when "experience" is interpreted as "learning through practice". But think about it instead from the viewpoint of the townsfolk: what people in general believe the character has learned to do. This is why you get experience when you return to town, where you or others can brag about your exploits and flash around treasure as proof of your accomplishments. XPs aren't all reputation; maybe there's a flat 1,000 xp worth of practice needed for each level, with the rest being reputable deeds. When they reach name level, XP requirements flatten out and is more or less the same for all classes.
Thus: the fighter is the standard, requiring 2,000 xp to reach 2nd level, with an additionall 2,000 to reach 3rd level. At 4th level, though, the fighter requires three times as much reputable deeds as mere practice. The magic-user requires the same amount of practice to reach 2nd level, but needs 50% more effort when trying to impress the locals. Why? Because magic is often subtle, especially 1st spells, and magic is a little distasteful. Magic-users aren't as respectable as fighters.
But around 5th level, where Fireball and Lightning Bolt first become available,the reputation of magic-users picks up. They still need more XP to reach 6th level (Magician) than a fighter needs to become a Myrmidon, but only a little more; to reach 7th level, they need less XP than a fighter. And while that 7th level Champion is struggling to reach Super-Hero level, the Enchanter will blow through two levels, becoming a 9th level Sorcerer before that fighter hits 8th level.
Clerics start out way more reputable, because they keep evil at bay through faith. It takes less XP for a cleric to reach 2nd level than it does for a fighter, and they stay on the fast track through the 6th level. But then it slows down; reaching 7th level is no easier for a cleric than it is for a magic-user, and it takes longer for clerics to reach 8th level than it does for magic-users, although it's a little faster than fighters. Fortunately, 8th level is name level for clerics, so advancement becomes flat for them from then on.
Thieves, of course, are even faster, reaching 7th level before either clerics or magic-users. However, this may be a side effect of lowering thief XP to reflect weaker abilities. Still, once they reach name level, their requirements flatten out to 125,000 xp per level, which is more than any of the other classes; this may be because their bad reputation catches up with them.
This interpretation does help to explain level limits, though. It's not that elves, dwarves, and halflings aren't as good as humans, but that there's a limit to how heroic such a character will seem to be in the eyes of the (human) population.