Symbolism, Imagery, Allegory
The black box is a physical manifestation of the villagers' connection to the warped tradition of the lottery. Jackson is pretty explicit on this point, when the subject of replacing the box comes up:
No one liked to upset even as much tradition as was represented by the black box. (5)
The townsfolk believe that this box may, in part, be made up of shards of the previous boxes, back to the OG black box. This is reminiscent of the practice of collecting Christian relics, like hair or bone from the bodies of the saints or pieces of the Cross. The lottery has become such an ingrained part of town traditional that it's become an affair with religious overtones.
But the box can also be read as almost a metonymy of the lottery itself. Like the lottery, the black box has no function except during these two hours every June:
[The black box] had spent one year in Mr. Graves's barn and another year underfoot in the post office and sometimes it was set on a shelf in the Martin grocery and left there. (6)
This alerts us to the fact that the purpose of the box, like the lottery itself, has become obscured by the passage of time. It's well worn, but the villagers are reluctant to let it go (again, like the lottery itself). In fact, we don't think it's too far-fetched to say that the villagers' treatment of the box represents their thinking on the subject of the lottery as a whole: they're a bit terrified by both the box and the lottery, but they're also too frightened (and, perhaps, fascinated), to drop either one.