What is "gregorian-calendar"
The gregorian calendar was promulgated by Pope Gregory XIII in October 1582, replacing the Julian calendar, which had been instituted by the Roman Emperor Julius Caesar around 46 BC.
The Janiano calendar considered leap years every four years and that caused a deviation in the years, reducing its duration to about 0.0075 days on average. Over the centuries this difference was accumulating and it was realized that this calendar was with a difference of about 10 days compared to the reality. This difference was noted mainly on special dates, such as the equinoxes of spring and autumn.
The Gregorian calendar was created to correct this difference by defining leap years as those divisible by four, except those that are multiples of 100 and are not multiples of 400. So 2016 is a leap year, as it is divisible by 4 (and not divisible by 100). The year 1900 is not leap because it is multiple of 100, but not 400. The year 2000, in turn, is leap because it is multiple of 100 and 400.
The change of calendars was instituted on 4 October 1582, and so it was followed directly by 15 October 1582 - the days between 5 and 14 were "skipped" to correct the distortion caused by the Julian calendar.
One detail is that not all countries have adopted this calendar at the same time. Greece, for example, only adopted the Gregorian calendar in 1923, so historical dates are often ambiguous, as it depends on which calendar was being used in each place, at each time.