The story of why Monday is Feb. 29 rather than Mar. 1 goes all the way back to at least 46 BCE, when Julius Caesar reformed the Roman Calendar.
Before that time, a Roman year was ten days shorter than our years are, and divided into lunar months. In order to keep the year in tune with the seasons, an extra month would be tacked on occasionally. Caesar noticed, however, that Egyptians used a calendar based on the sun rather than the moon. So, in consultation with the Alexandrian astronomer Sosigenes, he decided to create his own new system, hoping to solve the problem of the drifting seasons. Each solar year in the Julian calendar would be 365.25 days long. The months would have pretty much the lengths that we recognize today, and the shortest month would—as it does on Monday—get an extra day every four years to account for the annual accumulation of a quarter of a day.
To address the discrepancy between the old Roman calendar and the new one, Caesar made that first new year 445 days long. It would take decades for the new calendar to be widely observed, but the problem should have been solved. Except for one thing: an actual solar year is not 365 days and 6 hours long.
The average established by Caesar was only a little bit off—it was 11 minutes and 14 seconds too long—and Europeans kept using it for the next thousand-plus years. By 1582 though, those 11 minutes per year had accumulated to a 10 day discrepancy. This discrepancy interfered with calculating liturgical dates like Easter, which is set by the moon, so Pope Gregory XIII issued a Papal Bull to fix the problem. As a result, in the year 1582, Oct. 4 was followed directly by Oct. 15. Pope Gregory also set up a convoluted new scheme to prevent such a maneuver from being necessary in the future: Every four years would be a leap year, unless it was the beginning of a new century—except for every 400 years, when we would keep the extra day ("the exception to the exception," as TIME once called it).
Skipping three leap days every 400 years would keep the calendar and solar years in alignment, or at least closer to that goal—sometime near the year 4000 the current count will be one day off, as the current system is still 26 seconds ahead of the solar year.
But, although the Gregorian calendar—named for the Pope who developed it—was first introduced in 1582, England and its colonies didn't adopt the new calendar until 1752. By that point, the error was up to a whopping 11 days. That year, people went to sleep on Sept. 2 and woke up on Sept. 14. The change was made because, as TIME wrote in 1952, "Lord Chesterfield persuaded Parliament to give in to Gregory. 'It was not...very honorable to England to remain in gross and unavowed error,' he said, 'especially in such company [as Russia].'"
Some other holdouts didn't adopt the Gregorian calendar until the 20th Century, Russia among them. Indeed, that's why the Bolshevik coup of Nov. 7, 1917, is confusingly called the October Revolution.
The phrase "leap year," which probably refers to the jump in days of the week—a calendar date usually moves forward one day of the week per year, but it moves two days in a leap year—predates the Gregorian calendar, according to the Oxford dictionaries. But the history of all this leaping has continued to evolve in modern times, even as recently as 1972, when leap seconds were introduced. The advent of the atomic clock had led eventually to the decision to, per TIME, "[redefine] the basic unit of time—the second—in terms of the precise tuning-fork-like vibrations of the cesium atom." The new second would not always line up with the length of a solar day, because the Earth's rotation slowed over time, so a second could now be added or removed as needed.
As for why it took so long to get to this point, perhaps it was James A. Barnes of the National Bureau of Standards who put it best, back when the leap second was invented: "It takes time to agree on time."