Space and Physics
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Today is Leap Day. Every four years, an extra day is added to the Gregorian calendar (other, better calendars are available), making February 29 days long.
This hasn't always been the case, of course, as calendars have changed a lot over the years and across cultures. Before Julius Caesar introduced the Julian calendar in 45 BC, and with it leap days every four years, the Roman calendar had just 354 days. In order to keep the calendar lined up with the passage of the Earth around the Sun, this calendar had to introduce a whole new month every four years.
"[Legendary king of Rome Numa Pompilius] Numa, [calculated] the difference between the lunar and the solar year at eleven days, for that the moon completed her anniversary course in three hundred and fifty-four days, and the sun in three hundred and sixty-five," Plutarch wrote in the Life of Numa around the beginning of the second century CE.
“To remedy this incongruity [Numa] doubled the eleven days, and every other year added an intercalary month, to follow February, consisting of twenty-two days, and called by the Romans the month Mercedinus. This amendment, however, itself, in course of time, came to need other amendments.”
The Julian calendar was a vast improvement on having to add an extra month every four years, given that it changed to merely adding a day. However, it wasn't perfect.
In order to try and link the calendar up to the solar year (the time it takes for Earth to revolve around the Sun), the Julian calendar had a leap year every four years, in which an extra day was added. The problem was that since the actual solar year is 365.24219 days, the Julian calendar quickly (and by quickly, we mean incredibly slowly) gains a day every 314 years.
While this may not sound like much, by the time the Gregorian calendar was introduced in 1582, the year had drifted by 13 days. Adopters of the calendar tried to make up for this, but due to a miscalculation, only skipped 10 days instead of 13. To stop further drift, the Gregorian calendar continued with leap years every four years, but now skips them when the year is divisible by 100 and not divisible by 400.
Leap days and months are there to make up for our calendars not quite matching up with the solar year. As you have probably guessed, the main consequence of not having a leap year is that the days begin to drift. This animation from astronomer Dr James O'Donoghue neatly shows how that drift occurs.
This wouldn't have many real-world consequences, although it might be a pain for anyone whose work depends on the seasons (such as farmers) rather than arbitrarily setting dates for projects. It could also, as it did before the Gregorian calendar was introduced, really mess around with religious festivals. The Gregorian calendar was introduced after Easter began to drift away from the vernal equinox. Enough time without leap years, and you might find that Northern Hemisphere Christmas is in the middle of summer.
