Summary describes or reports with minimal detail, so you can cover a lot of information in few words. A flashback, on the other hand, reveals the past, but does so in a scene, which is a moment in time that unfolds in detail. Which you use depends on the nature of the background.
Use flashbacks to convey background information only when it is important for the reader to see how something happened. Flashbacks interrupt the unfolding of the narrative and should be used with care. They're often appropriate when background details are the motivation for action in the unfolding story. In Sue Miller's novel While I Was Gone, Joey Becker is a mother of three and the wife of a minister in a small town. As a young woman, she lived in a commune, a blissful experience that ended abruptly when one of her housemates was killed. When a friend from that commune comes back into Joey's life, she has to confront her past. Miller devotes whole chapters to flashbacks because the nature and nuance of that time is vital to understanding Joey's reexamination of her life.
Flashbacks can be important in short stories, too. In Mary Gaitskill's "The Girl on the Plane," John Morton's seatmate on the plane admits that she is an alcoholic. This prompts John to make his own admission: when he was younger, he raped his friend, Patty. He's not claiming innocence and he wants forgiveness, but he's also not convinced of his guilt. The action is firmly rooted in the events on the plane—his admission and his desire to be forgiven—but the nature of his relationship with Patty and the events leading to the rape are vital to the reader's understanding of John's state of mind, so they're rendered in flashback.
For information that the reader simply needs to know exists in the character's history, use summary. In Julie Orringer's "The Smoothest Way is Full of Stones," Rebecca stays with her aunt and uncle and her cousin, Esty, while her mother is in the hospital. She struggles to reconcile this household's new Orthodox practices with her own, less-strict upbringing. In one scene, Rebecca and Esty wade into the water up to their waists because they're not allowed to swim. Orringer summarizes Rebecca's history with Esty:
This is the kind of thing we used to do when we were little—the secret sneaking-off into the woods, the accidental wrecking of our clothes, things we were punished for later. This was when Esty was still called Erica, before her parents got divorced, before she and her mother moved to Israel for a year and became Orthodox.The reader does not need to see these childhood moments or Esty's transformation as they happen. In following Rebecca's emotional journey, it's simply important that we know this alternate version of Esty exists and that Rebecca is trying to make sense of this. The reader gets the necessary information without straying too far from the present moment.
Be careful to avoid the "information dump." A big chunk of background all at once—particularly when it's summarized—can be a drag to read. Include only what's necessary to understand the unfolding action in the story. And parcel it out. Even better, you can suggest background within the action of the story. If Lisa hesitates to get in the pool and keeps her distance from the edge, it will be clear she's wary. Her thoughts about the crashing waves at the beach last summer and the way it felt coughing up salt water may be enough to let the reader know she had a bad experience. Sometimes that's all the reader needs to understand the immediate moment.