A flashback is a structure technique writers sometimes choose to include incidents that occurred before the point when the story or novel begins. With a flashback, the setting of the story changes to an earlier time and sometimes to a different place.
There is another way, however, that a writer can include information about events that occurred before the beginning of the story. The writer can just tell us what happened before, or the writer can have a character tell what happened before, without actually changing the setting of the story. This structure technique is called "antecedent action."
In "The Open Window," there is no flashback; the setting of the story does not change. However, we learn the antecedent action from Vera as she talks to Mr. Nuttel. According to Vera, Mrs. Sappleton experienced a terrible tragedy when her husband and brothers went hunting and never returned. Furthermore, she continues to wait for them to come home. As the story develops and Mr. Nuttel runs away terrified, Vera explains to her aunt and uncle that Mr. Nuttel is a nervous man for once having spent the night in an open grave after being hunted by wild dogs in an Indian cemetery.
So, the antecedent action in the story consists of Vera's two stories, the disappearance of Mrs. Sappleton's family and Mr. Nuttel's horrifying night in a cemetery. It is at the conclusion of the story that we find out Mrs. Sappleton's "tragedy" never happened, and we know she is making up another wild story about Mr. Nuttel. None of the antecedent action included in the story actually happened, but Vera is a great story teller.