This day is generally observed as the appearance anniversary of Jesus Christ.
Krishna devotees also celebrate Christmas, in the mood of offering respect to Lord Jesus, a pure and empowered preacher of God consciousness. Srila Prabhupada, especially when speaking with Christian audiences, would often affirm that Jesus is our guru (teacher), because his whole life was focused on spreading love of God:
". . .we all have a great hidden treasure, and if we consult the oracle of Vedic literature we will find it. God is full of six opulences—all wealth, all knowledge, all beauty, all strength, all fame and all renunciation. We are His sons, and as such we have immense property to enjoy. In Bhagavad-gita Sri Krishna says that all living entities are His sons. If He is our father, and is such a rich father, then why don’t we reestablish our relationship with Him? Krishna sends His most intimate and confidential sons like Lord Jesus Christ to inform us of this heritage we have forgotten, to call us back home, back to Godhead. Unfortunately we are too busy consulting some mundane astrologers trying to find out what will happen to this body, trying to heal the body or make it last a few years longer, completely forgetting that this body is temporary and doomed to perish." (from "Krishna is the Proprietor of Everything" in Back To Godhead #46)
Many of Prabhupada's disciples originally came from Christian families. Here, Prabhupada offers some thoughtful and practical advice to one such disciple who was visiting his family during Christmas:
"Regarding the Christmas Day meal with your family, I do not think you should partake of the food prepared by non-devotees. Better you should prepare your own foodstuffs and offer to Krishna and then, if you like, you may offer these remnants to Lord Jesus. I think that Lord Jesus will also appreciate this. Of course you may sit down with your family and take fruits and milk which they offer but rather than taking the foods which they have prepared, you may prepare and offer your own prasadam for Lord Krishna, and then offer the same to Lord Jesus."
Pictured is Adorazione Dei Pastori by Domenico Ghirlandaio.