Typically, characters are described as either flat or round, static or dynamic. "Round" and "dynamic" are very similar in that they both describe characters who are complex and become even more so over time. Sammy is a dynamic character because he changes in the course of the story. After he quits, he realizes that his gallant actions have been lost on Queenie and that no one understands his chivalry. He decides that he will no longer be one of the "sheep" in his small town and will instead make his own way in the world.
If understand a "round" or "dynamic" character to be one who undergoes some sort of change over the course of a story (usually in response to a conflict he encounters), then Sammy from "A & P" is a round character. When we first meet him he seems to be a prototypically hormonal teenager, lustily eyeing three girls in swimsuits as they traipse through the supermarket in which he works as a cashier.
But then something interesting happens. The manager, Lengel, calls out the three girls for being inappropriately dressed. Everyone stops to stare as Sammy rings up the purchase while the "queen" of the group stands there, publicly embarrassed and humiliated. Wanting to be seen as a sort of hero willing to sacrifice his job to defend the girls' besmirched honor, Sammy tells Lengel "I quit," hoping that the girls hear him as they beat a quick path out of the store.
They don't, but Lengel does, and he gives Sammy a chance to retract his impulsive declaration. At this exact moment, the climax of the story, Sammy has a choice. He can meekly apologize and go back to checking the "sheep" through his grocery line, or he can stand on the principle that lay behind his hasty decision. He chooses the latter, and realizes - even though he doesn't quite have the words to express it - that he's the kind of person who will always be willing to sacrifice personal gain and security for integrity. That's why, as he steps out into the daylight, his "stomach kind of fell as [he] felt how hard the world was going to be to [him] hereafter."