Irony and foreshadowing are used to make the climax more powerful and disturbing.
Irony refers to something unexpected happening in a story. In this case, it is ironic that the people continue to gather and take part in this ritual, even though they do not really know why they are doing it. They do it because they always have. The reluctance to replace the tattered box demonstrates how they cling to tradition.
Mr. Summers spoke frequently to the villagers about making a new box, but no one liked to upset even as much tradition as was represented by the black box.
The reader knows that these people gather for this event because it is tradition, but the reader still has no idea what the event is. There are other little nudges of irony. Children are gathering stones alongside adults, where normally adults would discourage this behavior.
Foreshadowing is hints at future events. The tattered box, the three-legged stool, and Mr. Summers all foreshadow the importance of tradition and reluctance to change. The stones and uneasiness that everyone feels foreshadow trouble and a disturbing event ahead.
"Some places have already quit lotteries." Mrs. Adams said.
"Nothing but trouble in that," Old Man Warner said stoutly. "Pack of young fools."
The climax is the most interesting part, or the turning point. In this case, it is when the full irony of the story and the outcome of the foreshadowing is revealed. A girl is chosen to be stoned to death, and despite the senseless and horrific nature of the act, they do it.
This story is an example of artful use of foreshadowing to make an ironic climax more powerful. Jackson gives us little hints that lead to more and more information, but we do not really know until the end.