If a Cactuar Falls Alone in the Woods, Does Anybody Gain a Level?
What defines a level? While experience points can track progress in general, levels are reserved for measured, integral improvement. That's "integral" in the mathematic sense - i.e. related to integers, whole numbers that don't include fractions or decimals. Being halfway or even 99 percent of the way to mastering an ability has zero in-game impact. You either know it, or you don't.
Pretend your character just leveled and learned the Fireball spell, finally enabling you to really stick it to those ice gnomes or frosty wildebeests or whatever-the-hell your cold creature du jour is. It's a boon to your offensive powers, but consider this: You went from zero demonstrable knowledge in this spell to complete mastery in a single post-battle "ding!" That's the equivalent of not being able to read or write a single letter in spite of years of study, and then one day breezing through the complete works of Shakespeare in an afternoon.
This is more a consequence of game design needing to be fun than a lack of attention to detail. The alternative would involve you gradually mastering Fireball in tiny increments. Perhaps the first 10 times you cast the spell, you smoke up like a chimney without the fire. Maybe then you manage to conjure a few sparks or singe enemies with a candle-like flare, but a Great Chicago Fire-esque conflagration is still a long way away. When players' entertainment comes into play, however, games will always start with a bang rather than a whimper.
Further inspection reveals my boasted triple-digit HP has no real-world analogue. You could gain a thousand of the aforementioned levels and be no more equipped to survive a bullet or a hundred-foot drop than you were when you began. That's not to say different people can't take different amounts of "damage" before they end up at that great Game Over screen in the sky, but rather that it's not a negotiable value. I might be able to learn how to take a punch or two, but no amount of training will ever allow me to withstand the outrageous ordnance-unloading, dinosaur-stomping and planet-exploding endured by the average game character.
But with attribute points like Strength, Intelligence and Dexterity, the leveling analogy lends itself better to real-life growth. You can easily measure physical fitness as a result of time invested: Run for a month; shave minutes off your mile; level up! Pump iron for a year; double your max bench press; +4 STR! Even intelligence has plenty of rating frameworks in the form of tests, though intellectual progress will always be harder to measure than physical. But regardless of these statistical increases, remember: Merely making progress doesn't count as leveling. It's that integral leap that earns you your wings.
Now that you're primed on the underpinnings of these statistics, let's see if you can snatch the controller from my hand, grasshopper.