The Mayor of Halloween Town is, well, the Mayor of Halloween Town. His body (head included) is shaped like a cone. He wears a tall top-hat and suit with a spider bow-tie. He also wears a ribbon that says mayor on it. Being a politician, he is naturally "two-faced" and can rotate his head to appear as either happy or sad, depending on his mood of course.
Despite his office, the Mayor apparently has very little actual authority in the day-to-day running of the town, especially in planning for Halloween. This is attested when he arrives at Jack Skellington's house to discuss some plans with him, not knowing that Jack is not home. When Jack does not answer, the Mayor quickly gets hysterical and yells, more to himself than anyone, "Jack, please, I'm only an elected official here! I can't make decisions by myself!". Nonetheless, the Mayor seems to enjoy his position. He apparently owns the only automobile in town...., a hearse-like car called the "Mayor-mobile" that is equipped with a loudspeaker for making announcements and a black, cat-shaped hood ornament that sounds a siren when its tail is cranked.