In Shirley Jackson's short story "The Lottery," the black box symbolizes the foreboding that accompanies a ritualistic process the outcome of which is deliberately left unclear. Jackson sets the stage in a way that becomes apparent only in retrospect:
"...Mr. Summers...arrived in the [village] square, carrying the black wooden box, there was a murmur of conversation among the villagers...Mr. Graves followed him, carrying a three-leggged stool, and the stool was put in the center of the square and Mr. Summers set the black box down on it. The villagers kept their distance, leaving a space between themselves and the stool, and when Mr. Summers said, 'Some of you fellows want to give me a hand?' there was a hesitation before two men, Mr. Martin and his oldest son, Baxter, came forward to hold the box steady..."
The purpose of the black box is not yet apparent, but Jackson has imbued it with a sense of mystery or intrigue, and she emphasizes that its use dates back many years:
"The black box grew shabbier each year: by now it was no longer completely black but splintered badly..."; "'Seventy-seventh year I been in the lottery,' Old Man Warner said."
And, again, as Mr. Summers sticks his hand in the box to stir the slips of paper inside:
"Because so much of the ritual had been forgotten or discarded, Mr. Summers had been successful in having slips of paper substituted for the chips of wood that had been used for generations. Chips of wood, Mr. Summers had argued, had been all very well when the village was tiny..."
Jackson has established the setting: a village that has experienced growth over the course of many years, and that has its rituals and traditions that include the black box. A community event of some kind will take place -- an event that is part of the village's traditions. And we know that villagers have some trepidation regarding the black box, although that detail may not garner much attention until its purpose is revealed.
The black box figuratively and literally sits at the center of "The Lottery." Its contents condemn one unlucky villager to a violent, barbaric death -- the most resilient aspect of the ritual, a process most had begun to take for granted ("Although the villagers had forgotten the ritual and lost the original black box, they still remembered to use stones.")