The Gregorian Calendar, a modification of the previously used Julian Calendar, was first proposed by Neapolitan doctor Aloysius Lilius, and adopted by Pope Gregory XIII in 1582. The mean year in the Julian Calendar had exactly 365.25 days, but given that the mean tropical year duration is approximately 365.2422, every thousand years the Julian date is off by about 7.8 days.
The church was interested in having Easter celebrated at the correct time, so it was decided that the calendar would be modified. The fix was to define that years divisible by 100 will be leap years only if they are divisible by 400 as well. So, in the last millennium, 1200, 1600 and 2000 were leap years, but 1100, 1300, 1400, 1500, 1700, 1800 and 1900 were not. That gives a correction of 7 days. This millennium will have 8 days corrected.
The Gregorian calendar also fixed the first day of the year as January 1, which was already the first day used in Italy, Germany, and other places, but not universally (the British Empire, for example, began the year on March 25).
When the new calendar was put in use, to correct the error already accumulated in the thirteen centuries since the first church council of Nicaea, a deletion of ten dates was made passing from October 4, 1582 directly to October 15, 1582. This created some consternation, and the church was accused of stealing days of people's lives.
Not all countries accepted the new calendar immediately. The British Empire (including what is now the United States) didn't adopt it until 1752, by which time it was necessary to correct by eleven dates (September 2, 1752 being followed by September 14, 1752). Again, people objected to the change--not because they literally thought days were being stolen from their lives, but because they were paid only for days actually worked, but were required to pay a full month's rent for the shortened September, causing hardship. Russia did not accept the new calendar until 1918, which has the bizarre consequence that the anniversary of the October revolution now falls in November. There are groups inside most or all of the churches of Eastern Orthodoxy which did not accept the change to the new calendar. These Old Calendarist groups tend to assert that under the Julian Calendar the eternal liturgy in Heaven was reflected on earth by the liturgical calendar, and that the change meant that Heaven and Earth would be out of tune.
The Gregorian calendar can be extended to dates preceding its official introduction, producing the Proleptic Gregorian Calendar.