The day when September 2 was followed by Sept. 14
In 18th century Britain, there was a problem with the calendar.
Britain and its possessions, including the American colonies, used the old Julian calendar, begun by Julius Caesar in 46 BC. Meanwhile, Europeans were using the newer Gregorian calendar, introduced in 1582 by Pope Gregory XIII.
The problem with the Julian calendar was that it had an error built into it. The Julian calendar miscalculated the solar year by 11 minutes. This made an error of 1 day every 128 years. Not a big deal during one year, but over two thousand years the calendar spring moved increasingly farther away from the spring equinox, completely messing up the seasons.
In addition, different calendars complicated legal, contractual, and other business matters since there was always an issue with dates.
So in 1751, pursuant to the British Calendar Act of 1751, Britain (and the American colonies) made the "Gregorian Correction" in 1752. The act proclaimed that the day following Wednesday, Sept 2, should become Thursday, Sept 14, 1752, according to historic-uk.com.
It is a myth that there was rioting over a lost 11 days, probably inspired by a painting.
The act also provided that New Year's Day (and the change of year number) should fall Jan. 1 (instead of Mar 25) in 1752 and every year thereafter. As a result, 1751 had only 282 days.
