While it's not telegraphed, it's the fireflies that hatch out of the eggs. You are in Mystia's dream, and you're basically gathering parts of her dream (figments, wishes, and fears) in order to "hatch" them as something that gives you more influence over the dream.
The full idea was to have four stages, each with you entering a different character's dream. And they would have their own themed wishes and fears, as well as something else that hatches out of the eggs based on their character. (Ghosts for Yuyuko, foxes for Yukari...)