The short answer: In 1582, the Roman Catholic Pope decreed that a new calendar would be used. Catholic Europe adopted the new calendar, but Protestant countries did so much more slowly: Great Britain and her American colonies did so in 1752.
The Orthodox world, unconcerned with Catholicism, took little notice. However, in 1918, the Soviet Union adopted the new calendar – but the Church did not. In 1923, the Greek state and church adopted the new calendar.
Today the Orthodox Church in Russia, Jerusalem, Jerusalem, Sinai, and Mount Athos continues to use the Church calendar. Most of the rest of the Orthodox Church celebrates saints’ commemorations according to the new calendar. In practical terms, in our century, this means a thirteen-day difference – so we celebrate Christmas on December 25, which falls on the civil calendar’s January 7.