But let's start with the most basic question: What does level actually measure?
The obvious answer is "skill," but that's not actually any clearer. Skill with what? Two high-level Warriors in World of Warcraft can have totally different talent builds, but according to their levels, they're equally skilled at being Warriors. Does that mean that in-character, the dual-wielding berserker should be just as skilled in battle if he picks up a shield? Is he skilled with weapons in general? Armor in general? Why can't he wear certain armor until he's reached a certain level of skill? Skill is a useless term unless you specify where his skills actually lie -- otherwise, it's essentially just as vague as "level" was in the first place.
It's clear that level measures something, in-game and out-of-game. Many games won't let you perform certain tasks until you reach a certain level, and if you want to maintain some sense of verisimilitude, it's hard to believe that these tasks just became available all of a sudden. Surely there's something that happens, some sign that you've shifted from being a novice adventurer to being an experienced individual, unless it's easy for people in-world to see your level and assign you tasks based on it, but that's a bit too meta even for my sensibilities.
You might be wondering what all of this has to do with referring to your level in-character. The answer is that it's a simple matter of understanding what you're referencing in the first place. If it were as simple as gaining a pound each level, you'd just type out your weight and be done with it.
In some games, of course, there are options. There's some precedent for referring back to levels in Final Fantasy XIV, for example -- you have guilds built around given classes that provide some degree of structure, so you could easily say that the concept of level is part of the in-universe ranking system for adventurers. Some games even explicitly define it, such as the Security/Threat Level in City of Heroes. Of course, then it gets even stranger -- why does beating up a lot of criminals authorize you to access higher-security areas? There's a clear touchstone for levels, but no really good reason for their existence or why they rank up in a steady pattern.
In some games, such as the aforementioned World of Warcraft, you can try working around things a different way: abilities. In a game where a class at Level Y learns Ability A, you can have your character just say, "I know Ability A." This has the benefit of sounding a little closer to an actual person describing his or her talents, but it has the distinct disadvantage of assuming that the other person knows the ability list and the corresponding levels by heart. It's also totally useless with any abilities or skills that don't follow a very set pattern -- in RIFT, for instance, saying you have a given ability is less than useless because of the freeform structure.
A lot of players try just substituting "level" for another vague term. This pretty much never works, and even when it does it's a kludge. Try to avoid it.
Oddly enough, Star Trek Online handles this perfectly by virtue of its military structure. There's a distinct set of ranks through which players rise, each with a certain number of grades, and the whole system is tied intimately to in-universe systems. It does mean that you don't get the advantage of having, say, a character who's been promoted to a high station without any real merit, but you have to give the corner cases a bit of leeway. It's at least as solid a system as I've ever seen, albeit one that only works in a specific setting.
Unfortunately, much like with time, there's no real blanket method to fixing up all of these problems in a way that makes sense. What your level measures is something difficult to quantify, if in fact it's even possible to quantify. But you still need to be able to communicate it because in the game world, it's tied into age, skill, and prestige all rolled into one. If anything, the closest thing it comes to measuring is your progress through a story... and in roleplaying, that's a tricky thing to measure through numbers.
And when all else fails, just type something reasonable and bracket the number as OOC. It might be a bit ugly, but it works.
As always, feedback is welcome in the comments or via mail to firstname.lastname@example.org. Next week, let's talk about dancing with yourself, and the week after that I'm going to talk about when it's time to do something big and scary without having a clear plan.
Every Friday, Eliot Lefebvre fills a column up with excellent advice on investing money, writing award-winning novels, and being elected to public office. Then he removes all of that, and you're left with Storyboard, which focuses on roleplaying in MMOs. It won't help you get elected, but it will help you pretend you did.