The Julian Calendar was invented by the Romans (I think under the reign of Julius Ceasar). It was a calendar that had 365 days a year, except every 4 years was a leap year which had 366 days.
Sounds famililar? It sounds like the calendar we use today, right? Wrong! We use the Gregorian Calendar. We don’t have a leap year every 4 years… well, we kind of do, but we really don’t.
If the year is divisible by 4 it may be a leap year; You see, if the year is divisible by 100, it must also be divisible by 400.
For example, the year 2000 was a leap year. But the year 1900 wasn’t. And neither will the year 2100 be a leap year. (But in the Julian Calendar, years like 1900 and 2100 will be leap years.)
This error was discovered In the 16th Century when they noticed that the Vernal Equinox (1st day of Spring) was 10 days later than it was back in the 4th century (which was when the Council of Nicea was held and determined a date formula for Easter). So Pope Gregory XIII authorised the use of the new calendar (hence the name, Gregorian Calendar). Basically, people went to bed on Thursday October 4th 1582, and woke up the next day on Friday October 15th 1582.
Eventually, other parts of the world would adapt the Gregorian Calendar. But the Orthodox won’t accept this new calendar.
Since the 16th Century, there have been 3 more erroneous leap years in the Julian Caledar (1700, 1800, and 1900). Hence now, the Julian Calendar is 13 days out of whack. That’s why some Orthodox Churches celebrate Christmas 13 days later than us. (After the year 2100, they’ll celebrate Christmas 14 days later than us.)
(The Easter date formula has other factors involved. I’m not sure if the Orthodox use the Julian Calendar to determine Easter.)