Christmas day is the birth of our Lord. Boxing day and the following day (26/27th Dec) are devoted to praying to and praising of the Virgin Mary, who gave birth to our Lord and God (Synaxis of the Theotokos). On the Sunday after Christmas Day we celebrate James the Brother of Our Lord, David the King, and Joseph the Betrothed. Eight days after the birth of our Lord we celebrate the feast of his Circumcision: this is New Year (1st Jan); this is where he received his name and circumcision, thus fulfilling the Old Covenant.
Then we move on to the Theophany (6th Jan/also known as Epiphany). Where Christ revealed the Trinity through his Baptising of Baptism. This is when Christmas is actually over: this is known as the Twelve days of Christmas.
To the Reader:
Have a Blessed day and may God Bless you and your Family.