A very weird stat, seeing as stats are supposed to represent your character's physical or mental attributes.
Luck is usually interpreted as either random chance, a calculated risk paying off despite the odds, or divine favor of some kind.
I'd tie luck down to a religion system in a given RPG. RPGs tend towards polytheism, so devoting your character to a god of war could boost melee crit rate, or a god of commerce could increase your chance of succesful persuasion attemps, etc. Can be used to temporarily mitigate a build weakness without permanently spending stat or skill points. So you'd have not one luck stat but one for every skill.
E.g. if your wandering merchant character with max charisma and high speech/barter investments is required to brave a very challenging dungeon to advance the plot, making a sacrifice to the god of war would be good preparation.