Aristotle was important to our understanding of fiction because he studied the effects of drama (read his Poetics). He felt that drama was helpful for the observer because of its cathartic nature.
For example, if a person were to view a tragedy, the idea was that they would walk away with an understanding of why the hero or heroes were flawed.This experience would teach them not to make the same mistake or nurse the same flaws as the hero or tragic figure.
Aristotle's influence on fiction comes through several channels, but primarily it comes from his "Poetics." This first major work of literary criticism in the West still shapes our understanding of drama, and, to a lesser extent, all literary arts.
His emphasis on catharsis as a major function of the arts has long shaped discussions of what fiction should be and do.
Aristotle's definition of tragedy, which begins with " an imitation of an action that is serious, complete, and of a certain magnitude" shapes discussions of what a short story should be. It is implicit in discussions of high and low art. The discussions in "Poetics" about unity shape discussions of unity in the story, and so on. Such concerns show up in critical evaluations of "messy" novelists like Dickens.