Of old time the Eastern Emperor assisted at the Hours of Prime, Terce, Sext and None on certain great days, and among them, on the Vigil of Christmas; hence they were styled Royal Hours, which name they retain in the Byzantine Rite.
On this day, then, special extra-long services are held - or rather, just one super-long service, by concatenation - during which, not only are three proper psalms read at each of Prime, Terce, Sext and None, but at each are read a Prokeimenon (answering to a Gradual), then a Lesson, Epistle and Gospel. These amplifications of the normal Hours are celebrated with solemnity.
Those wishing to consult the texts, follow this link to the Royal Hours of Christmas.
There is also a Catechesis of St Theodore the Studite for the Nativity of Christ that is read at Byzantine Rite Prime this day: a beautiful patristic passage.