The term 'backstory', background story, back-story, or background is a set of events invented for a plot, presented as preceding and leading up to that plot. It is a literary device of a narrative history all chronologically earlier than the narrative of primary interest.
In Long Form improv, the backstory is obviously not pre-written but it can be exciting the reveal or develop a character's backstory by means of flashbacks, monologues or whatever. See Rendez-vous for a format where the backstory is pre-established.