"The Necklace" by Guy du Maupassant is the story of a just barely middle-class French couple, Monsieur and Madame Loisel. Madame Loisel is a pretty woman who believes her marriage to a mere clerk does not do her justice. She believes her face is her fortune and hopes to do much better. Her husband finally manages to get an invitation for them to a swanky affair, and after much fretting about what she has to wear to impress those at the ball, Monsieur Loisel sacrifices his savings for a new dress for his wife, and she visits a friend from whom she borrows what she believes to be a diamond necklace. After a successful night, Madame Loisel loses the necklace somewhere between the ball and home. The necklace is nowhere to be found. The couple must borrow money to replace the necklace and spend the rest of the story in debt and poverty. Madame Loisel loses even the smallest of amenities she enjoyed before. When she encounters her friend one day years later, she learns the necklace was a fake and not really made of diamonds at all.
That, of course, is the plot of the story, which may or may not be what you mean by asking what the story is about. On a deeper level, the story is about the problems incurred if one is more concerned about appearances than character, the damage done by dishonesty, and the importance of appreciating what one has. If Madame Loisel had attended the ball as her beautiful and natural self, none of this would have happened. Had she chosen what she thought was a more modest piece of jewelry or wore flowers instead, as her husband had suggested, none of this would have happened. Had she told the truth about losing the necklace right after she lost it, she would have learned how little it would cost to replace. All of Madame Loisel's "suffering" is a product of her wanting a life she does not have and her failure to appreciate what she does have. As the story ends, perhaps she does have some appreciation for what is now gone, thanks to her own attitude and choices.