The black box is indeed the main symbol. It represents tradition. The villagers are not sure about the box's history. They recall a chant and a certain handshake that used to go with it. Indeed the original box is tattered and worn, barely holding together. They did make some modifications, replacing wood chips with slips of paper as the villages population grew. The only thing they are really certain about is the use of rocks.
The Lottery, like the box, is shrouded in mystery. No one really knows why they conduct it (other than Old Man Warner making a reference to it having to do with good corn crops in June). They just follow along because it has always been done.
There has been talk of getting rid of the lottery, indeed some towns already have, and there seems to be some talk among the young people of junking the lottery. In this way the lottery is like the box. It is barely clinging together. But just as the villagers pull the box out once a year and go through the proceedings, observing what ceremonies and protocols they remember, they still obediently observe the lottery.
The black box in its delipidated state, needing to be refurbished, is symbolic of tradition. Just as in Romeo and Juliet and the Hatfields and McCoys where no can can remember how the feud started and why they continue fighting, no one can remember why or how the tradition of the lottery began except to say that it is for the assurance of good, healthy crops and that this is the way they've always done things.
Take a look at the names of the characters in the story as well. They are symbolic. Mr. and Mrs. Graves are two of the most important people in town--Mr. Graves helps run the lottery and Mrs. Graves is the first in line to throw stones. "Graves" sending people to their grave in each lottery.
Old Man Warner has been through the lottery seventy seven times. He "warns" against the craziness of getting rid of the lottery when he overhears some younger people speaking about nearby communities putting aside this tradition. He symbolizes tradition and complacency in body, character, and name.
I'll start things off for you by using the most obvious symbol in "The Lottery"l--the lottery itself. A lottery is traditionally a game, of sort, one which is associated with fun and success and chance--in the best possible way--and anticipation. Only good things can come from lotteries, and even someone who loses doesn't really lose much. It's more about the anticipation of something amazing to come. In this story, then, the lottery serves as an ironic symbol--something which begins in a harmless and sociable way but ends in tragedy. Several other symbols to consider are the stones, the black box, the stool, and all the other symbols which are represented in the lottery itself.
I would say it's the black box. It symbolizes the tradition that no one can clearly remember the how or why it started or why they continue to practice. It is old and shabby, falling apart, and the wooden chips have long since gone missing--now replaced by the black and white pebbles/marbles. The only thing people haven't forgotten is to get there early and collect enough stones to throw at the poor, unfortunate "winner" of the lottery.
The box is in need of renovation (like the practice of the lottery itself), but no one bothers. It is simply put up on the shelf and kept there safely until the next year's lottery is upon them.
The townspeople are symbolic of an unwillingness to challenge tradition and superstition. They might mumble about other villages who have done away with lotteries, but the consensus seems to go along with the old man who says that those other places are crazy for ignoring the old adage, "Lottery in June, corn be heavy soon." Their traditional actions, including having even the children of the condemned person throw stones, seem to ensure that this tradition of human sacrifice will continue into the foreseeable future.
I think you could argue that the stones operate on a symbolic function in this story - they are the means by which the lottery's "winner" is killed, and thus could be said to be a symbol of ignorance and indiscriminating mob violence. It is very interesting that the stones are presented at the beginning of the story as almost a game - the children gather them into piles, but it is only when we get to the end of the story that we realise their sinister purpose.
The black box is symbolic of the darkness of ignorance that plagues the citizens of the community. They are reluctant to replace it even thought it's older than the oldest participating member of the lottery. Just as the community is unwilling to give up the ignorance of the old ways for the enlightenment of the new ways like some of the other communities have chosen to do.
An additional symbolic meaning for the black box is the coffin.
The stones--"that token of preposterous time" as Golding writes in Lord of the Flies--is symbolic of the timeless predilection in people for violence.
The lottery--the word derives from the custom of drawing lots --itself is symbolic of the desire of people for a scapegoat.
Additionally, the setting of rural middle America is a symbol for the average citizen (more so at the time of the story's writing than in the 21st century, however). For example, an inner city setting would not have been as representative of the average American when Shirley Jackson wrote her fine short story.
Many symbols abound in the story from the character names of Summers to the black box itself. The symbols create great irony in what is happening and what will happen later in the story. The mark that the husbands have to make for their families on the paper can be symbolic also.
Thanks all! It really helped!