The Red Death may just be the biggest party pooper of all time. He's Death embodied, or something like that. It's not really clear just what he is, since there's no "tangible form" (touchable or solid form) underneath his costume. He doesn't seem to have any real motives besides bringing darkness and decay (and death) wherever he goes, particularly to fools who like to forget their own mortality. That may be why he's never invited to parties. But he always shows up, kills the host, and turns the whole thing into one deadly disaster.
He's not much of a talker, either. In fact, he doesn't say anything at all. When he shows up suddenly at midnight to Prospero's masquerade, he just starts slowly, silently "stalking" around, scaring people. (Notice how it's always "stalks," never just "walks"?) He doesn't need to do anything to scare people; his "costume" (and the stalking) is scary enough. Corpses with staring dead faces all covered in blood are creepy all by themselves.
The Red Death is not popular with Prospero's friends, who have shut themselves up just to avoid it. So everybody's outraged to see some guy show up in a Red Death costume. They just can't get over their disgust that somebody could show such poor taste. Until the man in the Red Death costume kills Prospero, and gets mobbed and unmasked. Then it turns out he's not a guy in a costume, after all – he's the real Red Death.