Well, obviously, magic. Because that is how they can exist. So how and what kind? Do they pour their own magic into the world and let it grow?
Perhaps they eat the odd vegetable, the odd bit of meat like an idiot warrior sent to destroy it? Maybe they eat the odd tree, or the clouds? To be honest they could eat anything.
Perhaps the magic they exude makes the world around them inedible? Or perhaps the magic that they exude makes everything edible, they just choose to eat to survive, they eat what is the least consequential in terms of magic. Maybe their purpose is to increase the magic in the world, to help it thrive?
Perhaps that is why magic is now something in our minds and hearts and not blindingly obvious in the world around us?
I have no idea, if I meet one, I will have to find out, if I live to tell the tale that is.