Eastern Orthodox Christians celebrate Christmas Day usually on or about January 7 each year. This is due to the fact that Eastern Orthodox follows the Julian calendar rather than Gregorian for liturgical feasts and occasions such as Christmas. So the date on the Julian calendar is December 25 but there is a 13 day difference so on the Gregorian or Western calendar it is January 7.
It is called the Gregorian calendar as Pope Gregory XIII proclaimed it in a Papal Bull in 1582. It was adopted by most Catholic countries but others did not use it right away (some for religious reasons since they were Protestant) and took over 300 years to be fully implemented. Great Britain did not formally adopt it till 1752. Russia adopted it in 1918, Greece in 1923 and Turkey in 1926. The reason for the change was the Julian calendar was not very accurate and had to many leap years. Because of this it would fall out of sync with fixed dates for astronomical events like equinoxes and solstices.
Eastern Orthodox Christians has over 250 million believers in Eastern Europe, Greece, the Caucasus, the Middle East, Europe, Africa, and United States. Except in countries that are predominately Eastern Orthodox, it is not celebrated as a public holiday.