Topic summary
Interactive narrative

Extracted from the Wikipedia article Story structure.
Interactive narrative
An interactive narrative is one which is composed with a branching structure where a single starting point may lead to multiple developments and outcomes. The principle of all such games is that, at each step of the narrative, the user makes choices that advance the story, leading to a new series of choices. Authoring nonlinear narrative or dialogue thus implies imagining an indefinite number of parallel stories.