Elementary, my dear Watson

There are two ways to explain a fictional quirk: you could discuss it from an in-universe perspective, or from a practical crafting point of view. Depending on which angle you're viewing the issue from, those explanations can be very different. This disparity makes it difficult to discuss points of confusion or potential problems in fiction, as people frequently end up talking at cross purposes, so the world of fandom has come up with the terms "Watsonian" and "Doylist" to better differentiate explanations within the universe from those of real-life circumstances.

Say, for example, that you notice an inconsistency in a certain character who had been wounded in the arm in the past but is now sporting an old leg injury. An in-universe (Watsonian) explanation could be that there were two separate injuries, or that the limp is a psychosomatic response to the arm injury. A likely real-life (Doylist) explanation is that the writer simply forgot where the injury was supposed to be. Doylism tells you why the inconsistency exists, really, while Watsonian explanations are a method of maintaining the text's internal consistency.