You know how dolls can be super creepy sometimes? Well, the Queen takes the creepy doll shtick to a whole new level. Seriously—she's so disturbing that Zach, Alice, and Poppy don't even play with her, instead having her rule over their fictional kingdom from a distance. All the other figurines get touched and moved and inhabited (the kids pretend to actually be them), but not the Queen.
The Queen just sits in the cabinet where Poppy's mom stores her. In this way, she's kind of like Poppy's mom—there but not. When Zach suddenly quits playing the Alice and Poppy without any explanation, it makes sense that Poppy offers up the Queen to lure him back in: Zach and Alice are the closest thing she has to a proper family in some ways, so she uses this symbol of her absentee mother to try to make sure she doesn't lose the little friend-based family she has.
And it works—Zach and Alice totally take the bait. When Poppy tells them she's dreamt that the Queen is possessed by a dead child named Eleanor Kerchner, the gang ventures out under cover of darkness to see if they can't help Eleanor rest in peace at last. The Queen, then, goes from not being an active player in the game (which matters—read up on the game as a symbol elsewhere in this section) to literally changing the kids' lives, ushering them out of childhood and into adulthood.
If you've read up on the game as a symbol elsewhere in this section, then you know that it represents life. Insofar as the Queen isn't a direct participant in the game, then, she represents something the trio is avoiding. That something would be adulthood, a terrifying presence that looms over childhood much like a creepy doll in a cabinet, until it can't be avoided any longer.
When Zach, Alice, and Poppy bury the Queen in a graveyard in the end, we know they're done hiding from growing up and ready to step into the next phases of their lives.