The Red Death is, well…death. Granted, it's a spectacularly gruesome form of death, probably calculated by Poe for maximum freak-out appeal. Think of it: having contortions and bleeding from all of your pores (particularly your face) until you die? Though as an image, there's something strangely stylish about it. After all, it's not as if the victims are drenched in blood. Judging from the Red Death's appearance, it's more delicate than that: the victims are sprinkled all over with it, almost "decorated" by it. It's grotesque (gross) and aesthetic (almost beautiful) at the same time – like the story itself.
But as far as symbolizing something goes, the Red Death is just a slightly revamped image of plain old Death. The story shows how it can't be escaped, and how Prospero's attempt to escape it is doomed.
Now why did Poe choose red as a color to be associated with death, rather than just the more obvious black? If he'd chosen black, he could have just gone with the "black death," (i.e., the bubonic plague that ravaged Europe in the 14th and 17th centuries – see more below) instead of having to invent his own plague. Our suspicion is that it's because red's a brighter and more dramatic color than black, and tends to increase black's own "freak out" effect when the two are put together (as in the red and black room). The story is bright and dramatic – with its colored rooms and its wild, whirling, costumed revelers. The effect of the imagery is almost dizzying. The red-black combo is really loud – it screams at you – so it fits well into that crazy aesthetic, which Poe might be using for a couple of different purposes (see below).
You might also wonder whether Poe based the Red Death on any real disease. Scholars have pursued that question. In general, they're interested in figuring out Poe's sources of inspiration for this story, and it certainly seems as if Poe's conception of the story was helped along by accounts of the Bubonic plague, also known as the "black death." Just like Poe's Red Death, it devastated the countryside of Medieval Europe beginning in the 14th century, and occasionally caused people to shut themselves up for protection from the contaminated. But the symptoms of the diseases bear little relation to each other, besides the fact that they're both fatal. For all we know, the Red Death is entirely fictional, conjured up by Poe, as we said, just for spine-tingling effect.