The Gregorian calendar is the calendar that is used throughout most of the world. It began being used in 1582. It replaced the previous Julian calendar because the Julian calendar had an error: it added a leap year (with an extra day every four years) with no exceptions. The length of the Julian year was exactly 365.25 days (365 days and 6 hours), but the actual time it takes for the Earth to go around the Sun once is closer to 365.2425 days (about 365 days, 5 hours and 49 minutes). This difference is about eleven minutes each year.[1]
This made the seasons get out of track with the calendar. For example, as the centuries went by, the equinox (when day and night are the same length) was happening earlier and earlier than its traditional date, March 21. It was the calendar that was wrong, not the earth's orbit. By the 1500s, it was starting around March 11, ten days 'too early' according to the calendar. To farmers, this did not matter because they worked to the seasons rather than to the calendar. But it mattered a lot to the Christian church because the date of Easter is calculated from the equinox being on 21 March. So Pope Gregory XIII declared that the calendar must skip ten days in 1582.
To make sure that the mistake did not happen again, they revised the 'leap year rule'. Until then, every fourth year had February 29, without exception. The change was that there would be no February 29 for every year that ends in 00 - unless it could be divided by 400. So the year 2000 was a leap year, because it could be divided by 400, but 1700, 1800, and 1900 would be common years, with no February 29.
The official change took place the following October, when Thursday, 4th was followed by Friday, 15th.