The necklace which Mme. Loisel believes is real is later revealed to be faux, (meaning false in French) just as the material values that Mme Loisel holds as of the greatest importance are false.
She dressed plainly because she could not afford fine clothes....She grieved incessantly, feeling that she had been born for all the little niceties and luxuries of living. She grieved over the shabbiness of her apartment, the dinginess of the walls, the worn-out appearance of the chars, the ugliness of the draperies.
So, in essence, the necklace underscores the theme that material possessions cannot bring a person happiness--a most relevant theme today.
That Mme. Loisel is entirely materialistic is evident from the beginning of the story until the end. When her husband brings home the invitation to the ball, thinking she will be delighted, she merely complains that she has nothing to wear. Then, when he sacrifices the money that he has been saving for a rifle and donates it for a new dress for her, she does not even thank him. Nor does she thank her husband for the years of sacrifice that he endures on her behalf. After Mme. Loise has returned the necklace and she meets Mme. Forestier in the park, selfishlessly she places blame upon Mme. Forestier for her hard years:
Yes, I've had a hard time since last seeing you. And plenty of misfortunes--and all on account of you!
Never does Mathilde Loisel appreciate the love of her husband and the friendship of Mme. Forestier. Like the necklace, Mme. Loisel is a person of falseness.
The title carries two meanings like many titles. Of course, its literal title refers to the actual necklace that Madame Loisel (Mathilde) borrows from Madame Forestier. The figurative title, though, refers to the symbolic weight around Mathilde's neck. First, she feels constrained by her lot in life. She longs for a life of leisure and beauty and feels that she has been shorted in life by being born into a family of common workers with no hope of escaping her social class. She believes that she has married beneath herself and thinks that
she suffer[s] endlessly, feeling herself born for every delicacy and luxury.
Mathilde truly thinks that if the "burden" of her lowly position in life were lifted off her (the figurative necklace) she would be content and would finally be where she should be society.
Additionally, the figurative necklace demonstrates the truth of Shakespeare's quote that "all that glisters [glistens] is not gold." Mathilde is so caught up in outward appearance that sheneglects to appreciate what she has. Her husband truly cares about her and wants her to be happy, but she just sees that he is a commoner--she doesn't seem to look inside and appreciate his true character. She also chooses the fake piece of jewelry from Madame Forestier's collection, illustrating that her idea of status and beauty is based solely on the exterior. She unfortunately does not realize what true class is.
The necklace is a symbol of the entire story, isn't it? What does the necklace represent? It represents Mme. Loisel's longing to be something she is not, just as the necklace itself pretends to be something it is not. The necklace also represents the Loisels' years of toil for something that is not even real. Also, as the story itself, the title is ironic. The reader begins, believing that a necklace is going to be very important in the story, and then goes on to see that the necklace, for all its importance, is a fake. The reader does not see the irony until the very end of the story, just as Mme. Loisel does not understand how and why her life has been so bitter for the past several years. The necklace is simply a "thing," but it symbolizes how our longing for another life, with material objects, can seduce us into decisions with dire consequences. I hope you are able to have a bit more insight now into why this is such a good title for the story.