Buckle up, this is going to be a doozy of a ramble. (Don't worry, there will be a TL;DR summary at the end.)
I was ruminating this morning on the difference between RPGs, where your characters get permanently stronger over the course of the game, but if you die, you're dead; and platformers (think Sonic, Mega Man) where you never actually gain raw power, but if you "grind" so to speak you can accumulate lives/continues that allow you to stave off your "game over" screen. (In particular, I was imagining the Mecha Sonic/Death Egg Robot battle at the end of Sonic 2.) I was thinking, how is this fair? If you're not good enough to beat Mecha Sonic, how are more chances going to help you?
Then the light bulb went off: experience. Not experience points, as in an RPGs, but actual literal experience. By the time you've spent 12 lives on Mecha Sonic, hopefully you have a better idea of his attack pattern, you react more quickly, and you're able to defeat him, because you, as a person, gained experience fighting him. I came to realize that this is the concept that RPG developers imply with their systems. The simplest ones reward you with experience (points) for killing enemies, suggesting that your characters got better at attacking and defending, learned about the enemy's characteristics, and are therefore stronger for it. Some games also award you experience for discovering new areas, opening treasure chests, solving puzzles, etc., which is one step closer to the real-world connotation of "experiencing" something. Then there's the direct route of games like FFII, where experience is abstracted (or rather...concreted?) from generic "points" into specific actions. This really makes a ton of sense, on the surface, but implementation can be awkward.
Going back to the "points" system, though, here's where it doesn't make a lot of sense: grinding. Don't get me wrong, I love a good grind in my RPGs. But each enemy, generally, gives you the same amount of experience whether you kill it for the first time or the 1000th time. But by the 1000th time you've killed an any, you know what you're doing; you know your weapons and defenses and abilities; you aren't really gaining anything that maps to real-life experienceaside from, yeah, another battle took place. (This is, of course, somewhat ameliorated by the fact that level requirements typically increase so that you can't easily become an all-powerful titan by killing Fangs in the Evil Forest.)
What would an RPG look like where "experience" most closely mapped to the real-life concept? I think you'd definitely get boosts for all the little non-combat things like exploration, questing, and discovery because those are new experiences as you do them. As far as combat though, what if the experience was tied to the bestiary like in the FFXIII games? As you battle an enemy, your bestiary fills in as you try out different spells and attacks on it. That's literal experience: you find out that an enemy is weak to fire by casting fire on it. In a sense, that is its own reward, as it makes subsequent battles with that enemy easier and doesn't offer any more "experience" the 1000th time you cast fire on the enemy. But imagine if your level progress was tied to your bestiary progress; the more you know about your foes, literally the more experience you have with them, the stronger you are. (I'd also throw in the II-esque system of getting better with different weapons by using them.)
TL;DR: "Experience points" are sometimes, but not always, linked to the real-life concept of "experience". Should they be more directly linked? What would that look like? Have some games done this better than those I mentioned?