I'm guessing that your question refers to "The Masque of Read Death" by Edgar Allen Poe as you didn't state which story you were referring to, so I have edited your question to make it slightly clearer.
When considering this tale, you need to consider that this is an allegory - a narrative that is really a double story. One story - the main story of Propsero inviting his guests to avoid the pestilence and therefore death by living in his castle luxuriously until the disease passes. The other story lies under the surface and characters and events represent abstract ideas or states of being - Animal Farm is a superb example of allegory in novel form.
Red, then, in this short story, can be taken as a symbol of blood, death, and an echo of the "Read Death" - the disease that is rampaging through the land. It is perhaps key to focus on the fact that the 7 rooms end with the 7th room in black, with windowpanes that are scarlet: "a deep blood colour". We can see therefore that the 7 rooms can be viewed as the seven stages of life, with this last room representing death. It is also significant that the rooms start off in the East and progress to the West - mimicing the rising and setting of the sun, which supports this allegorical interpretation of the rooms and the colour red.