If your character does a certain action (X), you get a benefit (Y) which may improve your character.This rule, or rather a subset of this rule, is included in the original game.
- X is "kill a monster or retrieving treasure"
- Y is "get 100 xp/HD or 1 xp/gp, and increase your level at certain xp breakpoints"
People who complain that D&D is unable to handle every kind of fantasy sometimes point to the "kill monsters or take their stuff to get xp" rule as one example of how D&D can't handle, say, James Branch Cabell's Jurgen. Well, OK, I've never heard anyone suggest Jurgen as an example of fantasy that D&D can't handle; usually, it's something that's really so very close to default D&D, it seems like quibbling over nothing. But yeah, "kill monsters" is not very close to the spirit of Jurgen.
But X can be changed. "Defeat (not necessarily kill) a monster" is already a reasonably common house rule. "Defeat without killing" is also possible. Or what about "convince another character to kill or take treasuer"? What kind of fantasy would that support? (I'm thinking "intrigue". Let's you and him fight!)
And Y can be changed. If it were "roll the smallest die that is greater than your level, and increase your level by 1 if the roll is higher," you have random advancement. If you change both X and Y -- "successfully perform a hard task at the limit of your ability at least once in an adventure" paired with "roll above your ability at the end of the adventure to increase that ability," you get something very much like Runequest/BRP. X+Y could even be "spend gold for training at the end of an adventure" and "roll d100 less than (gold)/level/100" for a purely practical form of advancement.
The idea is that the stripped-down rule of "perform action X, get benefit Y" can be applied to many more forms of fantasy than the purely mercenary forms of D&D.