What is a scapegoat? How does this relate to symbolism? How does it relate to the story?
According to Wikipedia, the scapegoat was a goat that was driven off into the wilderness as part of the ceremonies of Yom Kippure, the Day of Atonement, in Judaism during the times of the Temple in Jerusalem. The rite is described in Leviticus 16. Since this goat, carrying the sins of the people placed on it, is sent away to perish , the word "scapegoat" has come to mean a person, often innocent, who is blamed and punished for the sins, crimes, or sufferings of others, generally as a way of distracting attention from the real causes.
In the case of "The Lottery," the scapegoat was the person who was lucky enough to win the lottery by choosing the black stone. He/she was the target of the the stoning or sacrifice killed for the purpose of ensuring a bountiful harvest. It was a barbaric practice that went back so far that no one could remember when, where, or exactly why they still practiced it. The "scapegoat" is symbolic of the carthartic cleansing of the community--a symbolic washing away of sins and evils which would bring bad luck for the coming harvest and new year. The box itself is worn to the point of almost falling apart--symbolic of the tradition, and also of the death of the "lucky" person since it is a black box.