Symbolism, Imagery, Allegory
For Clara's birthday, her mother gives her a necklace that initially seems like a beautiful, enviable gift. It's a pretty locket with gemstones, and it's obviously valuable and expensive. But, when she opens up the locket, she finds something rather morbid inside:
Against an ivory background was a weeping willow tree, less than an inch high. Each branch and front was fashioned from snippets of human hair. "Ah, so this is for mourning! The hair is from your dead brothers and sisters, I suppose." (5.26)
The thing about the locket is that it's just like everything else on display in the Wintermute home—a somber reminder of the four Wintermute children who died. Instead of being celebrated for her individuality and cherished, Clara is always being forced to live up to the memory of her dead siblings, and she's never allowed to have fun or forget that they are a family in mourning. Even seven years after her four siblings died, Clara still has to go visit their graves all the time—including on Christmas.
Even though she loves her deceased siblings, all of this focus on death is depressing for Clara, and she cannot live out her life as a normal, happy child. In the end, though, Clara tears off her locket and throws it at Grisini in order to buy herself time to save Parsefall and Lizzie Rose:
With one hand she broke the chain of her birthday locket. Then she shrieked, "Take it!" and hurled the locket at Grisini. (46.19)
In throwing away the locket, Clara isn't just shedding a material possession. She's also letting go of this imposed state of mourning that she's been in for the last seven years and finally making decisions that matter to her and make her happy, like inviting Parsefall and Lizzie Rose to come live with her.