A side story in fiction is a form of narrative that occurs alongside established stories set within a fictional universe. As opposed to a prequel, sequel, or interquel, a side story takes place within the same time frame as an existing work.
Side stories are common in epic type series, especially war oriented series where it is possible to tell many stories from many different points of view. It is typical for side stories to be self contained, small scale events, insignificant in the bigger picture. They tend to be one shot stories with a beginning, middle, and end and focus heavily on character drama while the major action occurs mostly in the background.
A side story is not quite the same as a spin-off. A spin-off takes already known characters, usually supporting or background characters and involves them in a story or series which highlights them and further develops their character. The series' true main characters may make cameo appearances or be referred to in dialogue. Side stories, rather, focus on a completely new set of characters who have no history and typically no connections to the existing main characters and the settings for side stories are intentionally away from the major events that we know our main characters to be participating in
An example of a side stories occurs in the U.C. Gundam universe. The OAVs Gundam 0080:War in the Pocket and the Gundam:08th MS Team are stories set within the same time period of Mobile Suit Gundam's One Year War but have nothing to do with the characters or situations from Mobile Suit Gundam.
The term side story seems to have come out of anime fandom, and most side stories are anime-related. It is a direct translation of the Japanese word gaiden which is often used to describe such stories. But the term could be loosely applied to some non-anime works.
The Doctor Who universe includes many short stories in which the Doctor has no part but are clearly intended to depict events in the fictional universe he inhabits. Examples include the BBV video Auton Trilogy series and Dalek stories such as the Big Finish Productions audio series Dalek Empire.