The exposition of a short story is the necessary background information for understanding the plot of the story. It usually includes description of the setting, characters, previous events (maybe) and of course, the conflict.
The exposition for "The Masque of the Red Death" then is as follows. The story takes place in an unspecified place and time, but likely takes place in the past as the land is ruled by a prince who lives in a castle and the first place of refuge sought is an abbey (setting). There is a plague in the land that causes victims to bleed from the pores before dying. This plague spreads and kills very quickly (main conflict).
Prince Prospero (main character), in an effort to protect himself and a group of his followers, secures an abbey in which they all enter and remain safely inside for several months.