The main external conflict is clearly between Prince Prospero (and his guests) and the deadly plague—the Red Death of the title—raging outside. The Red Death has already caused appalling devastation, claiming the lives of many victims. The last thing that the prince and his guests want is to be the latest additions to that long and growing list. So they shut themselves up inside Prospero's castellated abbey walls, engaging in riotous partying to take their minds off the terrifying plague that stalks the land.
Prospero's internal conflict is with his own sense of mortality. The appearance of the mysterious scarlet-clad spectral figure appears to have wrecked his meticulous plan to keep the Red Death well away from his imposing stately home. Locking himself away deep inside the walls of the abbey was not just a way to keep out the plague; it was also designed to postpone Prospero's inevitable confrontation with his own mortality. Like most of us, Prospero doesn't want to think about death, even though he knows it's inevitable. But the appearance of the spectral figure forces him to confront the reality of his own mortality, with truly terrifying consequences.