In Shirley Jackson's short story, "The Lottery," the black box, the names in the box, and the black spot are symbolic elements in the story.
The color black is associated with death. Pall bearers often wear black arm bands. People who attend funerals wear black (or navy blue). For many years, families in England wore black for a prescribed amount of time while in mourning, especially depending upon one's association to the deceased. (I.e., the prescribed time of mourning was different for a brother than for a spouse.)
The black box may well symbolize judgment and/or death. In the story, every name of every person in the community goes into that box. No one is exempt, not even Mr. Summers and Mr. Graves. Death will come to someone whose name is chosen from that box.
The names are symbolic of those who will be judged. In the big picture, the name of the person to die comes from this group of names, so we can surmise that the list represents mankind, for all will die, and many people believe all will be judged at that time.
The black spot is a sign of death. There are two things that come to mind. First of all, during the plague in Europe (called "The Black Death"), people who were infected developed a large circle on their bodies, often in several places. These "buboes" became black spots as the symptoms of the disease spread and, ultimately—for the most part—ended in death. On the other hand, in pirate lore, specifically after Robert Louis Stevenson wrote Treasure Island, the black spot on a piece of paper spelled a summons or doom for whomever received it. In Treasure Island, two men receive the black spot on a piece of paper. "The Lottery" is much older, but in one of The Pirates of the Caribbean movies, Jack Sparrow discovers a black spot on the skin of his hand, spelling his doom—this probably also comes from pirate lore—though probably from Stevenson's time.
In the story, "The Lottery," the black box symbolizes the judgment of the members of the town. The list of names represent those who will be judged—one of whom will die. The black spot is symbolic of the person from the town who is chosen to die. All three items relate to the story's themes of custom and tradition, violence and cruelty, and victim and victimization. As symbols, they foreshadow the seriousness of this day, which at first is presented as just another pleasant day when the members of the community get together, laugh and visit—with no inkling for the reader of the terrible activity they will soon all be involved in.
In an historical context, the story was written in the 1940s with a backdrop of World War II and man's inhumanity to man. Jackson's husband, literary critic Stanley Edgar Hyman once commented on his wife's writing.
'Her fierce visions of dissociations and madness, of alienation and withdrawal, of cruelty and terror, have been taken to be personal, even neurotic fantasies. Quite the reverse: They are a sensitive and faithful anatomy of our times, fitting symbols for our distressing world of the concentration camp and the bomb.'
While it might seem that the story was appropriate when written, the sad truth is that not that much has changed. We still have wars; humans are still uncaring of the plight of others; and, societies across the globe still demonstrate man's inhumanity to man. "The Lottery" is a timeless, haunting piece of literature.