Magic is real. All it takes is the right time, place, and circumstances... a wish, a sacrifice.
Eddy the Unicorn was brought to life thanks to the correct ritual taking place--however, the child who summoned him had vanished, unaware they even conjured him. He'd spend ages searching, only to learn the child who dropped the ice cream cone in the ritual space had been a tourist leaving in a hurry, and would likely never find them.
He had to learn to fit into modern society, picking up a job at a diner, where his large size would make for a rather snug fit on the uniform. This circumstance worked in his favor, however, and he is part of the reason people go to said diner now.
While his hair isn't ice cream, his hands and feet are truly made of caramel, meaning he can use them for fun foreplay as well as a treat. The trade off, however, means hot days can be a bit of a bother...