On October 15th, 1582, the Gregorian Calendar started.
The previous calendar, the Julian Calendar, had, by this time, become rather out of alignment with the actual year. As a consequence of this, ten days were skipped in October, with October 4th being followed by October 15th. Other changes were also made to the calendar to keep the alignment, such as the modification of how leap years are calculated.
The Gregorian Calendar is named after Roman Catholic Pope Gregory XIII. As it was enacted by a Pope, it had no authority outside of the Catholic Church and the Papal States, so it was only originally enacted at that time by four countries, Spain, Portugal, much of Italy and the Polish-Lithuanian Commonwealth. It took some time before countries that used the Julian Calendar adopted the Gregorian. For example, the British Empire didn't adopt it until 1752.
Image: Lavinia Fontana [Public domain], via Wikimedia Commons (commons.wikimedia.org/wiki/File:Gregory_XIII.jpg)