The symbolism of the necklace is made more apparent given the title of the short story is named "The Necklace." Therefore, the necklace, itself, is central to the story.
Given that Mathilde cannot go to the party without jewels, the necklace represents both her greed and artificial nature. First, Mathilde's inability to be satisfied with only a dress, her need for the necklace proves her greed. Compounding this, Mathilde is not happy at first with the choice of jewelry Madame Forestier offers her. She actually asks if there are any other necklaces.
By the end of the story, readers find out that the necklace if fake. The fact that Mathilde wore it like it was real, needed it to appear important (and not what she was), shows her artificiality. The necklace, therefore, represents Mathilde herself: both look like they are worth more than they actually are.
Let's examine how the symbol of the necklace is used in the story. At first it is seen as something of value that is desired and yet out of one's reach. In the end of the story, it's true value is revealed and it is "fake". We can expand this symbol to include anything that we might strive for in life? The question becomes "Is this really real?" or am I sacrificing things of true value for something that in essence is worthless? If the necklace represents "status" in one's life is it really something we ought to value?
The the symbol of the necklace speaks to the difference between appearances and reality. It asks us to question what it is we value and to develop the ability to be truly discerning in embracing those values.