The first paragraph of the story describes the disease which has been sweeping through the country ruled by Prince Prospero, a disease called "the Red Death" because "Blood was its Avatar and its seal -- the redness and the horror of blood." In other words, the disease caused such a profusion of blood to leak out of its victim that the color of blood has been chosen to be a part of the disease's name. It is a truly frightening disease that moves quickly and is always fatal: "No pestilence had ever been so fatal," and the whole progress of the disease from one's contraction of it to one's death lasted only about thirty minutes.
Some scholars believe that the Red Death is symbolic of tuberculosis, an often fatal disease that eventually causes its victims to spit and cough up sometimes copious amounts of blood. Tuberculosis took Poe's mother when he was only three years old (he actually watched her die of the disease), as well as the beloved woman who took him in after his mother's death, Mrs. Allan, and eventually, his young wife.
Prince Prospero is ironically described as "happy and dauntless and sagacious" -- his actions hardly paint him as brave and perceptive -- and when half the people in his country had been taken by this disease, he invited one thousand friends to hole up in his castle with him and basically have a giant party until the disease had run its course outside the castle walls. Party-goers felt that "The external world could take care of itself." The story begins about five or six months into their isolation.