What is Gregorian Calendar?

Legal Definition
The Gregorian calendar is internationally the most widely used civil calendar. It is named after Pope Gregory XIII, who introduced it in October 1582.

The calendar was a refinement to the Julian calendar involving a 0.002% correction in the length of the year. The motivation for the reform was to stop the drift of the calendar with respect to the equinoxes and solstices—particularly the vernal equinox, which set the date for Easter celebrations. Transition to the Gregorian calendar would restore the holiday to the time of the year in which it was celebrated when introduced by the early Church. The reform was adopted initially by the Catholic countries of Europe. Protestants and Eastern Orthodox countries continued to use the traditional Julian calendar and adopted the Gregorian reform after a time, for the sake of convenience in international trade. The last European country to adopt the reform was Greece, in 1923.

The Gregorian reform contained two parts: a reform of the Julian calendar as used prior to Pope Gregory XIII's time and a reform of the lunar cycle used by the Church, with the Julian calendar, to calculate the date of Easter. The reform was a modification of a proposal made by Aloysius Lilius. His proposal included reducing the number of leap years in four centuries from 100 to 97, by making 3 out of 4 centurial years common instead of leap years. Lilius also produced an original and practical scheme for adjusting the epacts of the moon when calculating the annual date of Easter, solving a long-standing obstacle to calendar reform.

The Gregorian reform modified the Julian calendar's scheme of leap years as follows:

Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100, but these centurial years are leap years if they are exactly divisible by 400. For example, the years 1700, 1800, and 1900 are not leap years, but the years 1600 and 2000 are.

In addition to the change in the mean length of the calendar year from 365.25 days (365 days 6 hours) to 365.2425 days (365 days 5 hours 49 minutes 12 seconds), a reduction of 10 minutes 48 seconds per year, the Gregorian calendar reform also dealt with the accumulated difference between these lengths. The canonical Easter tables were devised at the end of the third century, when the vernal equinox fell either on 20 March or 21 March depending on the year's position in the leap year cycle. As the rule was that the full moon preceding Easter was not to precede the equinox, the date was fixed at 21 March for computational purposes and the earliest date for Easter was fixed at 22 March. The Gregorian calendar reproduced these conditions by removing ten days.

To unambiguously specify the date, dual dating or Old Style (O.S.) and New Style (N.S.) are sometimes used with dates. Dual dating uses two consecutive years because of differences in the starting date of the year, or includes both the Julian and Gregorian dates. Old Style and New Style (N.S.) indicate either whether the start of the Julian year has been adjusted to start on 1 January (N.S.) even though documents written at the time use a different start of year (O.S.), or whether a date conforms to the Julian calendar (O.S.) rather than the Gregorian (N.S.).

The Gregorian calendar continued to use the previous calendar era (year-numbering system), which counts years from the traditional date of the nativity (Anno Domini), originally calculated in the 6th century by Dionysius Exiguus. This year-numbering system, also known as Dionysian era or Common Era, is the predominant international standard today.
-- Wikipedia
Legal Definition
Pope Gregory XIII instituted it in 1582 to replace the godless, prevalent Julian Calendar. Julian lost a quarter day every year. The papal-named solar calendar is now used all over the world. To keep the calendar in sync with the way the Earth moves, every normal, or nonleap, year has 365.25 days. Every fourth year is given 366 days and called a leap year.
Legal Definition
One making January 1st the beginning of the year instead of March 25th.
-- Ballentine's Law Dictionary