The Julian calendar was introduced by Julius Caesar in 45 BC and was the standard calendar of the Western world for over 1,600 years. It was replaced by the Gregorian calendar from 1582 because it drifted from the seasons. It is still used by some Orthodox churches for liturgical dates — and currently runs 13 days behind the Gregorian calendar.
The Julian calendar adds a leap day every four years, making the average year 365.25 days. But the true solar year is about 365.2422 days — so the Julian calendar is ~11 minutes too long, drifting about 1 day every 128 years.
By the 1500s this drift had pushed the spring equinox about 10 days off. In 1582, Pope Gregory XIII introduced the Gregorian reform: it dropped 10 days and refined the leap-year rule (skipping 3 leap years every 400 years).
The gap has since grown to 13 days, which is why Orthodox Christmas (25 December on the Julian calendar) now falls on 7 January Gregorian.
Several Orthodox churches — including the Russian, Serbian, Georgian, and Jerusalem patriarchates — still use the Julian calendar to calculate fixed feast days.
This is why "Orthodox Christmas" and "Old New Year" are celebrated 13 days after the Gregorian dates.
A small number of communities use the Revised Julian calendar, which currently aligns with the Gregorian calendar.