In Serbian and Russia and Jerusalem as well as Orthodox Church January 6th against 7th eve is Nativity (The day in which we Orthodox Christians, celebrate The Incarnation (Birth) of Christ).
In the Orthodox Church, there are some Orthodox Churches who celebrate Nativity on 24th against 25-th December (Bulgaria, Greece, Romania etc.) and some who celebrate Nativity on 6-th against 7-th January (Russia, Jerusalem, Syria, Serbia, Ethiopia, Egypt etc.) . The reason for this is some autocephalous (nation wide) Orthodox Churches use the so called New dates Church calendar, and others are still using the Old Calendar. Nomatter that all Orthodox Churches are in eucharistic (sacramental) communion and celebrate Easter on one and same date. The feast of birth of Christ was known to be originally celebrated on 24-th against 25-th of December (but this was according to the previous dates calendar used in the world which was based on the moon phases). After whole the world accepted and use even till now the so called Gregorian Church calendar, which is said to be more mathematically precise some of the national Orthodox Churches, with the usual consent between all nation Orthodox Church Patriarchates decided to move the 24-th against 25-th December to be celebrated on 24 to 25-th eve to be more accurate with the world dates calendar used by all throughout the world. This same 24-th against 25-th of December according to the old world dates calendar which was used in most Christian countries before the Gregorian calendar become the de-facto standard for world calendar coincides with 6-th against 7-th December.
There was quite a talk going around between people who were for and against the 24-th and 25-th calendar, as in all Orthodox Churches until the 1950/60 Nativity of Christ was celebrated on 6-th against 7-th January. Now there are two camps of people in the one Holy Apostolic Orthodox Church, those for the new calendar and those against it.
Actually in practice following Christmas on both date is not incorrect, and it should be mentioned in very ancient times of the Church, Nativity of Christ was celebrated every-day as Church services were continuing 10 to 12 hours each day!!!! Thus in ancient Church, there was not a special day for a birthday of Christ, but it was known in the Church Christ for sure Christ was born in December, many saints (if not mistaken) including st. John of Chrysostom said 24-th eve is the correct date on which the most pure Mother of God Virgin Mary gave birth to our savior and Messiah (Christ).
No-matter about the date, even as situation now is where some Churches celebrate Christmas on 24th eve and some on 6th against 7th this should not be perceived as separation of the Church, but as point of unification and increasing of possibility of people to hear about the birth of the savior of us the sinful humanity. As the good news of Nativity is preached and heard by unbelievers and believers twice the year instead of just one, making the world remember twice about the moment in which we received the news for hope of redemption and salvation from the corruption of death that ruled over us before Christ's incarnation and salvation mission on earth.