The irony of the story is that there are no real superstitious elements. Both the townspeople and Ichabod Crane, however, enjoy reading or hearing about old legends and stories of the supernatural, and this strongly colors their thinking and influences their behavior.
Crane is a schoolmaster and supposedly well-educated, so one would think he would be too rational to fall for folktales of ghosts and headless German soldiers, but he is an effete, backward looking type who revels in stories of the supernatural. The practical, all-American Brom Bones takes advantage of Crane's superstitious nature to set up a practical joke to drive Crane out of town. Crane thinks he sees the headless horseman, but the story makes it clear he saw some sort of fake "supernatural" creature made with a pumpkin. Once Crane is gone, Brom, who has outwitted him, can marry Katrina, the young woman they both love.
At the end of the story, we are given a rational explanation of what happened to Crane: he started over...
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