Once upon a time, around the year 525 during the reign of Pope John I, a monk named Dionysius invented the idea of Anno Domini by producing a calendar which marked the time since the birth of Christ. The numbering of the years was adopted for the Julian Calendar, a calendar created 600 years previous under the reign of Julius Caesar. The Julian Calendar allows for 12 months, 365 days per year, and 366 on leap year, once every 4 years. The numbering of the years would change with Anno Domini.
The calendar lost 11 minutes per solar year, then over time, 3 entire days out of every 400 years, so that by 1582 under Pope Gregory, a new calendar was issued that made that correction. Now, under what is known as the Gregorian Calendar, a leap year will happen every 4 years, and on years divisible by 400; but not on years divisible by 100. 1900 was not a leap year, but 2000 was.
But there was a bigger problem in the concept of Anno Domini. There was no year zero. A kid born on 1 BC would be 3 years old by 3 AD. But if you subtract, you get the wrong answer: 3 − (-1) = 4, and this is because there is no year zero in the calendar. For the Dionysian calendar, the counting is: -1, 1, 2, 3, rather than -1, 0, 1, 2, 3. The blame cannot be laid at the feet of Dionysius alone, however. Dionysius did not know of the number zero, because the number had not been known to the Romans, nor the Greeks, and not even the Church, for hundreds of years.
Well, it kind of did. The Arab world had known and used the number in their counting system since at least the days of the Greeks, and possibly before. Aristotle stated that there was no such a thing as a vacuum, and thus the very idea of zero, or of “nothing” as being countable, was anathema to Greek philosophy. Greek geometry, with all of its laws and proofs, had to proceed without it. They were aware that zero was being used by the Babylonians, but the Greeks had a good thing going with their pursuit of philosophy and didn’t want it being messed up by the introduction of zero.
This meant that the Romans, who did not pursue philosophy so much, had no zero in their rather cumbersome number system. And the Catholic church, who embraced Aristotle, had no zero for hundreds of years, and didn’t even question Aristotle’s idea of a vacuum until the 13th century. While the Catholics liked a rational God, and pursued philosophy and mathematics in their monasteries during the so-called “Dark Ages”, and even started the university system some time after the 10th century, did not see until much later how zero could actually fit in with their theology regarding “the void” and “the infinite”.
In the meantime, a calendar had been produced that had no year zero. This meant that centuries so not begin at multiples of 100, they have to begin at 100 + 1. While everyone was euphoric over the year 1999 becoming the year 2000, really the 21st century didn’t begin until 2001.