Irony is the pivotal force that pushes the plot forward. Shirley Jackson uses it to contrast the dark reality of what is really about to take place in the village, versus the facade of normalcy produced by the idyllic setting, the "civilized" citizens, and the seemingly peaceful day in June. 

Irony also drives the plot forward in the way that the author uses subtle actions and events to anticipate what is actually going to take place: One of the villagers will have to pick a name from a black box. If his or her name is selected, then that villager will be stoned to death by the others. There is no reason for it, except for an old rationale dating back to more than many years ago, regarding crops. 

To pique the twist even further, Jackson even infuses irony into the dialogue of the characters. Sure, one of them will be dead in less than an hour, but why take the humor away from the small talk? 

"Thought we were going to have to get on without you, Tessie.” Mrs. Hutchinson said, grinning, “Wouldn’t have me leave m’dishes in the sink, now, would you, Joe?” and soft laughter ran through the crowd as the people stirred back into position after Mrs. Hutchinson’s arrival.

Just think: The "position" was that of getting ready to select names. Tessie was late because, as it is universally accepted, she did not want to be there. She had an inkling that her turn may be on this day. Therefore, to show up late was to give fate a push. 

Of course the biggest irony comes in the end when, even those related to Tessie, just grab the rocks and go straight to the stoning, quite excitedly, as it would occur with the rigor of any other typical tradition. 

[...]The pile of stones the boys had made earlier was ready; there were stones on the ground with the blowing scraps of paper that had come out of the box Delacroix selected a stone so large she had to pick it up with both hands and turned to Mrs. Dunbar. “Come on,” she said. “Hurry up. “

Therefore, the irony accentuates the tragedy of the situation taking place, and exacerbates the dreadful feeling of knowing that this horrid and savage practice could still take place in civilized society.