Early civilizations attributed the evil of their society symbolically to one member of the group, either human or animal. This creature was then killed so that the society could be rid of evil, thus allowing a better future for those who are left. In Shirley Jackson's "The Lottery," the black spot, then, is the mark of evil; the paper is contained in a black wooden box in which the ballots were made the night before and the spot made with the "heavy pencil in the coal-company office." (Coal in the slippers at Christmas is from Prince Rupert, the devil, for the bad children.)
On the day of the lottery, the person who holds the paper with this carbon spot of evil is designated as the "scapegoat." That someone should be chosen in such an arbitrary way seems absurd, but the adherence to this dark ritual points to the irrational mob psychology of people, perhaps even suggesting the psychology of the Nazis who were capable of mass genocide since Jackson wrote this story in 1948.