The funerary monument of Pope Gregory XIII (r. 1572-85) was carved between 1715 and 1723 by Camillo Rusconi (1658-1728). The relief on the urn depicts the promulgation of a new calendar in 1582, the most significant achievement of the pope's reign.
The old calendar, which aligned the civil year more closely to the astronomical year, had been introduced by Julius Caesar in 46 BCE. In the Julian calendar, each year had 365 days, and an extra day was added every 4 years to make up for the six-hour difference between the civil and the solar year. The Julian calendar was a great improvement on what had gone before, but it had one fundamental flaw, it fell short 12 minutes each year. Over the years the missing minutes added up and by the beginning of the 4th century the spring equinox, which the Julian calendar had set at March 24th, was falling on March 21st. This was to have significant implications for the celebration of Easter, the most important feast in the Christian year.
In 325 the Council of Nicaea set the date on which Easter was to be celebrated as the first Sunday after the first full moon after the spring equinox. As the centuries passed, the date of the spring equinox fell back further and further; by the start of the reign of Pope Gregory XIII, it had fallen back to March 11th. The pope decided to act and appointed a special commission of experts to devise a system which would correct the error of the Julian calendar.
On February 24th, 1582, Pope Gregory XIII issued the bull Inter gravissimas, whereby the new calendar was to be put into effect. In addition to fine tuning leap years*, the bull also decreed that the ten days from October 5th to October 14th were to be eliminated, in order to offset the shift of the spring equinox.
The Gregorian calendar came into force in Italy, France, Spain, Portugal and Poland on October 15th, 1582. However, it was not accepted by Protestant nations until the 18th century.
*Aloyius Lilius (c.1510-76), the brains behind the Gregorian calendar, came up with the idea of adding an extra day in years divisible by 4, unless the year is also divisible by 100. If the year is also divisible by 400, an extra day is added, regardless.
Sadly, Lilius's ingenious method of aligning the civil and solar years is not perfect and the system is still off by 26 seconds. As a result, the Gregorian calendar will be a full day ahead of the solar year in 4909.