The necklace could very well be just a necklace, but it could also be something more. It's so flashy and beautiful, and so seemingly valuable. Despite its convincing outside, it turns out to be "false." It's all show, in other words, with no substance. Doesn't that description sound like it could fit any number of other things?
For one, you could easily read the necklace as a symbol of "wealth" itself – flashy, but false, in the end. Like "wealth," the necklace is the object of Mathilde's mad desire. Perhaps the revelation of the necklace's falseness at the end is meant to mirror the falseness of Mathilde's dream of wealth. Having wealth is not worth the trouble, any more than the false necklace was worth ten years of poverty. Then again, wealth has its advantages: it certainly seems to do wonders for Mme. Forestier's looks, for instance, while poverty ruins Mathilde's.
Maybe that connection between wealth and looks is a telling one. Even deeper than wealth, the necklace might represent appearance, the world in which it's the outside that matters. Wealth belongs to the world of appearance, because money buys glamour. Mathilde's unhappy because of the way her own shabby house looks, and the way her lack of money prevents her from wowing the people she wants to wow with her natural charm and good looks. The necklace is glamorous, and it also gives her the opportunity to be the woman she wants to be, for one evening. Beneath the fancy exterior, though, the necklace is not worth anything – it's a fake. In that respect, it fits Mathilde's own situation at the party: though she fools everyone there, she's not really wealthy. At the end of the day she is still a clerk's wife in a fancy party dress with some borrowed jewels.
The fact that the necklace is a fake may or may not have some kind of moral meaning. You could take it to mean that wealth, or appearances more broadly, are false. Against the backdrop of wealth and appearance, we have the contrast of Mathilde's poverty. Being poverty stricken may ruin her appearance, but it forces her to become responsible and hard working, and perhaps makes her appreciate what she had before. You could take away a moral such as, wealth just keeps you wanting more until you ruin yourself, while poverty teaches appreciation.
Then again, Maupassant never comes out and gives us this moral explicitly. And it's up to the reader to decide if giving up good looks, comfort, and your own personal maid for a work ethic and a little more appreciation is a good deal. After all, the world of wealth and appearances may be false, but it's still kind of fabulous. Just like the necklace.