Simply put, Medusae is a technical name for jellyfish. It's also the nickname given to the offworld-visitors responsible for the sudden expression of elemental abilities in Earth's children. The aliens looked like jellyfish - exceptionally large jellyfish, and so without anything else to call them, a reporter christened them Medusae.
They're a source of confusion and contention among humans. Nearly twenty-five years out from first contact (if you can call it that), The Great Illusion (the year when the sky turned pink and purple) seems like it might never have actually happened. Sure there are people who remember it, but memories can fade and fail, and no one born since that time has ever seen one of these strange creatures... officially.
So the big question becomes did the Medusae actually exist, or was it something else that got blamed on aliens because it was convenient? And if they are real, what do they want? Why did they change Earth's daughters, or was that an accidental by-product of their presence and evacuation?