The black box being kept in different locations signifies what?

The black box that holds the lottery tickets is getting old and splintered, and yet nobody has the heart to repair it. Likewise, nobody wants to take ownership of this box. Therefore, it wanders from place to place. People increasingly want to shove it to one side and forget about it. However, they can't: the box is described as "underfoot."
All of this shows the growing anxiety the villagers experience about continuing the lottery. To repair the box and make it as good as new would feel like a commitment to a ritual the villagers have begun to question. Likewise, to have a set spot for the box would enshrine it and lend it a dignity the villagers no longer are sure it deserves.
It is the elderly townspeople, like Old Man Warner, who are the great defenders of the lottery. Other people in the town note that nearby villages have ended their lotteries. The treatment of the box therefore symbolizes the ambivalence the townspeople feel about the ritual.

We learn that the box is very old, as it's been in use since before Old Man Warner, the town's oldest citizen, was born. It's in bad shape, splintered and cracked and chipped, and Mr. Summers sometimes talks about replacing it with a newer box, "but no one liked to upset even as much tradition as was represented by the black box." The box seems like a symbol of tradition then, especially of traditions that are held onto even when they no longer make sense or seem of value. In regard to its location, the narrator tells us that during

The rest of the year, the box was put away, sometimes one place, sometimes another; it 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.

It seems that, by changing the location of the box each year, it can never become an object one is used to seeing. Its location never gets familiar or comfortable, and the box is always visible, keeping it and what it stands for presently in mind no matter whether the lottery is soon or not. If the box represents tradition, then changing its location would make it seem like this tradition cannot be forgotten. If it were forgotten, then people might start to think that it isn't all that important (after all, they'd forgotten about it). However, with its changing location, people can never quite forget it, and this will make the tradition it represents seem more relevant all year long.