A cave makes us think of many things—hiding, protection, safety, and darkness, to name a few—and caves have long been thought of as places for reflection and knowledge, especially since Plato's Allegory of the Cave (which includes pretty much everything). And this is certainly true in our book.
Think about: The cave is where the members of the new Order gather, learning about each other and themselves and the magical realms, all while safely tucked away from the rest of the world with its grueling expectations for how young women should behave. It is a place the girls use to protect their secrets, whether they're stealing sips of alcohol or making their way into the realms, and though the cave leads them toward plenty of danger, it is also a place where it's safe for them to be themselves.
But the cave in our book also symbolizes something else: Gemma. Check this passage out:
Generations of rain have smoothed the stone to such a high sheen in some places that I catch a fractured glimpse of myself on its uneven surface—an eye, a mouth, another eye, a composite of ill-fitting pieces. (12.3)
Pro tip: Whenever a character in a book sees their reflection, we as readers are being clued into a moment of truth. Reflections are very often symbols for true selves in books (and movies), and the moment described above is no exception. Gemma understands herself to be "a composite of ill-fitting pieces"—a daughter without a mother, a clairvoyant in a non-magical world—and because the cave offers this truer reflection of her (instead of an intact image like a mirror might), we can see that the cave itself is part of the truth that's being reflected back to our main girl.
Not sure what we're talking about? Worry not. We'll explain. There's more to Gemma than meets the eye—we can think of her secret powers here, but also of how opinionated she is in an era when young women are supposed to keep quiet, and other similar qualities—and since the cave wall is what's below her reflection here, it symbolizes what's going on below her skin, or inside her.
Remember all that stuff we said at the start of this little analysis section about how caves symbolize hiding and darkness and safety and such? Well now would be a good time to apply that to Gemma's inner life. She has a certain darkness to her—how could she not after finding her mother stabbed in the street and watching her father succumb to opiate addition?—and she carefully guards both her true feelings and her secrets. She is a cave in her own right, slicked smooth on the outside by the unending expectations of the world, and much deeper than one might initially think.