Usually, narrative causality
refers to the sequence of events in a story
of any medium, be it book, movie, or play.
But as any fan of Terry Pratchett and his Discworld series of comic/satirical fantasy novels can tell you, Pratchett uses the term narrative causality to also refer to the "power" of story archetypes and cliches. Pratchett himself states, in Witches Abroad, that on the Discworld, "a story, once started, takes a shape... a thousand heroes have stolen fire from the gods, a thousand wolves have eaten grandmother, a thousand princesses have been kissed." For example, the youngest of three sons will always be the most fortunate, even if he's a naive simpleton (ESPECIALLY if he's a naive simpleton). Dogs chase cats, and cats chase mice (though Greebo, Nanny Ogg's cat, will chase just about anything that moves). Long-lost heirs to the throne are always turning up to reclaim their kingdom, often from some evil tyrant (thought there is the matter of Carrot Ironfounderson of the Ankh-Morpork City Watch). I'm sure you get the idea.
Pratchett uses the concept of narrative causality to both comedic and dramatic effect in his Discworld series, mostly by dryly commenting on the cliches that erupt regularly. When a plan absolutely has to suceed, people sometimes go to great lengths to ensure it's EXACTLY a million to one shot (since million to one chances always pay off). He also uses story cliches as a vehicle for dramatic irony, by generating characters that, either consciously or unconsciously, defy these cliches. Carpe Jugulum features as its villains a family of vampires who have managed to shed many old weaknesses and myths about vampires, much to the chagrin of those who try to ward them off with garlic or a holy symbol. On the dramatic side, Pratchett's Witches Abroad and Lords and Ladies (both featuring his character Granny Weatherwax, a hard-nosed witch who hates seeing people feel they have to live their lives based on fairy tales) invite us to wonder about the influence stories have on our lives (in the form of memes). After all, how many women have hoped (however faintly) to be whisked away by their knight in shining armor; and how many men have sought to be the one to rescue the damsel in distress, or be the Chosen One?