Narrative design is how something is structured and presented to tell a story. Literally every film has the same structure: The beginning with a rising action, the middle with a climax and then the end with a falling action.
Allen Feldman said "The event is not what happens. The event is that which can be narrated."
Narrative as an animator is creating a narrative for an animation that solves a problem.
Nancy Duarte said "The audience does not need to tune themselves to you - you need to tune your message to them."