Why do we have leap years?

A leap year exists to fix a fundamental mismatch: the Earth takes about 365.24 days to orbit the Sun, not a tidy 365. That quarter-day left over each year adds up, and if ignored, the calendar would slowly drift out of sync with the seasons, roughly a full day every four years, so that after a few centuries summer would fall in what the calendar called winter. To correct it, we add one extra day, February 29, every four years, which absorbs the accumulated quarter-days and keeps the calendar locked to the seasons.

But 365.24 is not exactly 365.25, so adding a day every four years slightly overcorrects, and the rule has a refinement most people never learn: century years are skipped as leap years unless they are divisible by 400. So 1700, 1800, and 1900 were not leap years, but 2000 was, and 2100 will not be. This extra tweak, part of the Gregorian calendar reform ordered by Pope Gregory XIII in 1582, keeps the calendar accurate to within a day over thousands of years. The system traces back to Julius Caesar, who introduced the leap year in 46 BC with the Julian calendar; his version added a leap day every four years without exception, which was close but drifted slightly over centuries, which is exactly the error the Gregorian century rule later fixed. So leap years are the calendar's patch for the awkward fact that the solar year refuses to be a whole number, and the fiddly century rule is the patch for the patch.