This is a very interesting topic, maestro, because, although the term is used with slightly different meanings in the text-based arts – prose, plays, and screenplays – I think the combined sense of those meanings is what good fiction is all about, and describes what we might strive for as novelists.
In novels, I’ve always understood it to imply a hidden meaning behind the text, an extra layer of complexity or possibility that complements the ostensible theme of a piece (whether or not there is one).
Theatrical directors sometimes use the word similarly to describe what they see in plays that makes it possible to keep interpreting and re-interpreting the good old standbys of their canon, while their actors have to be mindful of it to perform the new angle accordingly.
In screenwriting they use the term to describe the scene-by-scene subtleties within carefully-crafted dialogue that speak volumes about characters and their situations (in conjunction with the skill of actors, director, cameraman, editor), where they don’t have the advantage of narrative to describe what’s going on inside the actors’ heads. It’s subtext that helps you ‘feel’ a movie in your heart as you’re hearing the dialogue.
There’s a good article about its use in screenwriting
here, analysing a scene from ‘As Good As It Gets’ (one of my personal top 5 movies).
Given that a novel effectively becomes a movie rolling inside the reader’s head, the best writing, the good stuff that drags us into the page and stays with us long after we have experienced it, is riddled with subtext of all the above types.
In particular, I think a good grasp of subtext in the screenwriting sense is of great value to us as novelists. Pointed, economical dialogue reduces the need for narrative, and frees up our slim quota of qualifying adjectives and adverbs for use in action- and setting prose.
I like this quote from Logan Pearsall Smith, the great essayist:
What I like in a good author isn't what he says, but what he whispers.