The Emperor is never described, beyond this epithet, but several characters refer to him, particularly in The Lion, the Witch and the Wardrobe. Aslan and the White Witch both assert that both the 'Deep Magic from the Dawn of Time' and the 'Deeper Magic from Before the Dawn of time' are magical laws of the Emperor. Manifestations of the Deep Magic and Deeper Magic are crucial plot points in the novel. Mr. Beaver describes the White Witch as 'the Emperor's hangman', referring to her claimed right to execute traitors.
In subsequent books, the only characters who mention the Emperor Over the Sea are those who remember, or have researched, the long-past events of The Lion, the Witch and the Wardrobe. In particular, he is not mentioned in the creation story of The Magician's Nephew. In The Last Battle, Peter banishes the demon-god Tash 'in the name of Aslan and Aslan's great Father the Emperor-Over-the-Sea.
It is never made explicitly clear which sea the Emperor is beyond, or whether he actually exists. The books, however, describe only one sea in the world of Narnia, and when the crew of the Dawn Treader try to cross it, some believe they will find Aslan's Country on the other side; and indeed, they find Aslan and the end of the world at the uttermost east.
C. S. Lewis asserted that Aslan was Christ manifest in Narnia, rather than an allegory for Christ in our world. In The Voyage of the Dawn Treader Aslan comes very close to saying this explicitly: "Lucy, you can find me also in your world, but I carry a different name there. Your experience with me here will make it easier to find me in your world". This would imply that the Emperor is a reference to the Christian conception of God-the-Father.