As stated in the previous answer, the black box symbolizes death. The color black is associated with death and mourning in the Western world. Most of the villagers fear the black box. Out of it, a death sentence comes. After it is placed on a stool for the ritualistic drawing of the lottery slips, we are shown the villagers' fear and awe.
The villagers kept their distance, leaving a space between themselves and the stool.
The box also symbolizes a superstitious ritual that has outlived its usefulness. The villagers now use a second box made out of pieces of the first, but even this one is starting to fall apart.
The black box grew shabbier each year: by now it was no longer completely black but splintered badly along one side to show the original wood color, and in some places faded or stained.
All of this description symbolizes how outworn this ritual is.
The text is at pains to show that the villagers have forgotten much of the ritual. They change it when they need to: for example, they have replaced the original wood chips in the box with slips of paper. The box has no set home during the year but is stored with different people, including Mr. Summers, Mr. Graves, and Mr. Martin on his grocery shelf. This shows that the community as a whole is complicit in hanging onto this tradition, even as it grows more careless in maintaining the details of it.
The box, splintered, rebuilt, faded, and stained, symbolizes the way people will hang on to a destructive practice far too long. The villagers clearly could make a decision to change the central sacrifice that the box symbolizes into a more symbolic and less destructive ritual. We know this because they have changed other aspects of the ritual. Yet they go on mindlessly clinging to the most destructive aspects of a superstition. The story as a whole encourages us to look at what mindless rituals or destructive traditions we might want to get rid of in our own society.