The Snow Queen is a magical being that recides over the season of winter. She lives in a large castle made of ice in a place where the snow always falls.
Through outside interference, her two goblin servants make it so that her magical mirror is shattered, scattering the pieces all over the world. And while most of them are gathered up and returned to her castle, some of them come in contact with human beings, often with ill effect.
One of these humans is Kay himself, who gets a piece of the mirror lodged into his eye, where it continues making its way towards his heart, all the while making him more and more emotionally cold. At a loss for anything else to do, the Queen brings him back to her castle, most likely to save him from the effects of the mirror shard.