Analepsis is often referred to as a flashback, when some event from the past appears in a narrative out of its place in chronological order. Authors often use analepsis to share background information that the reader might need to better understand a character or something happening in the story's present.
Prolepsis is often called flashforward, when a story jumps ahead in time to some future date, skipping the intervening chronology. An author might use prolepsis in order to show a reader the outcome or consequence of something that happens in the story's present.
Poe does, in fact, make use of prolepsis in the story "The Masque of the Red Death." Initially, Prince Prospero is introduced, and we learn that he has gathered one thousand of his healthiest and most fun friends to quarantine themselves with him in one of his isolated abbeys. We are told that the prince has stocked the abbey with everything the group might need to entertain and enjoy themselves for a long time. "All these and security were within. Without was the 'Red Death.'" These sentences conclude the second paragraph of the story, and the third paragraph begins with the line, "It was toward the close of the fifth or sixth month of his seclusion [...] that the Prince Prospero entertained his thousand friends at a masked ball of the most unusual significance." Thus, we have skipped ahead in time some five or six months as, evidently, nothing very significant to the story happened in that time. Rather than bore us with unimportant particulars, Poe uses prolepsis. It is also important, it seems, to note that time has passed because the people within the abbey would, by now, believe themselves to be safe from the disease.