Symbolism, Imagery, Allegory
The mirror that Turtle Heart makes for Elphaba as a child helps to "illuminate" (pun intended) themes of sight and witnessing in this book. And themes of sight are also interestingly linked to childhood here.
As a child, Elphaba is captivated by the mirror. Aside from Turtle Heart, she is the only member of the family who can see things in it. What's more, these two characters can also fully understand what they are seeing. Looking into the mirror prompts Elphaba to say her first and favorite childhood word, "horrors":
She held it in two hands, and stared at it with one eye closed. She peered, she squinted; her open eye was distant and hollow. Reflection from the starlight off the water, thought Frex, hoped Frex, but he knew the bright vacant eye was not lit by starlight. (1.8.124-5)
As an adult, Elphaba not only loses her mirror, she also loses the ability to fully "see" as she did as a child. Instead she becomes ruthlessly practical, denying the existence of souls, other worlds, "Unnamed" and unseen gods, and occasionally magic itself. The adult Elphaba who has lost the mirror becomes blind in a sense, and she's aware of that fact. She often describes herself as not "visionary" (184.108.40.206) or as lacking in imagination or a sense of deeper meaning to things.
When Elphaba regains the mirror from the dwarf, she is only able to see the present in it. Again, her adult vision has been truncated. But it's notable that she gets the mirror back at a time in her life when she is revisited by people from her past, learns more about her family history from Nanny, and starts exploring memories from her youth. What sight she regains seems related to her regained access to her past and her youth.
But mirrors aren't just for seeing events and places; they are also for seeing the self:
"She thought: the Witch with her mirror. Who do we ever see but ourselves, and that's the curse." (5.11.21)
Ultimately, Turtle Heart's mirror represents the ability not just to see the world but to understand it, and to understand one's place in it.