Having been a bit of a lurker recently I've noticed a rise in the terms, 'Doylist', and 'Watsonian' when referring to opinion based replies or to describe character thoughts, feelings and reasoning behind actions.
The most recent version of this can be found in the comments on this question here:-
The TARDIS is quite capable of making up her own mind. She's sentient, sapient, and emotionally bonded to our protagonist. She is perfectly aware of what the Doctor is leaving behind. She is giving him her support. In addition to and along with the mementos, she is also leaving behind the very same thing as the Doctor. That's as much Watsonian explanation as I need for the obvious Doylist symbolism. – Gary Botnovcan 19 hours ago
The question here being, what do these terms mean precisely?