The place: an A&P grocery store in a small Massachusetts town. The time: a Thursday afternoon in the early 1960s. Sammy, the 19-year-old narrator of "A&P," notices three bathing-suit-clad girls enter his store, which is otherwise mostly populated with middle-aged housewives.
Yes, the conflict is just an extension of the initial situation. People just didn't wear bathing suits in indoor public places. Sammy observes regular A&P customers shocked by the girls' choice of dress.
Things were going OK until Lengel the manager showed up. The girls are in Sammy's checkout lane preparing to pay and be on their way. But Lengel feels the need to tell them they aren't dressed right for the A&P
Sammy doesn't like the way Lengel treats the girls, so, after ringing them up, he quits his job. This is certainly a climactic moment in Sammy's life – the first time he's ever quit a job, and the story's big emotional moment.
"A&P" isn't really long enough to build much suspense, but there is a moment when we wonder whether Lengel will call Sammy's bluff and Sammy will stay at the A&P.
Sammy quits, leaving his A&P gear on the counter.
The story ends with Sammy alone outside in the parking lot. As he watches his ex boss through the windows doing his old job, Sammy feels a sense of dread, a feeling that quitting his job really will make things harder for him in the future.