Leap Year as we know it was introduced in the Gregorian calendar, which replaced the old Julian calender in the 16th century (leading to many headaches for historians dealing in that period, who constantly have to cite dates in two ways.) The ancients knew a complete revolution around the sun takes slightly more that 365 days, and the early Greeks actually had a more accurate calendar than the one that replaced it, dictated by none other than Julius Caesar. That calendar added on a leap year every four years, which, over the centuries, caused the month and date to drift further and further from the ordinal equinoxes and solstices. 
The Gregorian calendar was named after Pope Gregory XIII, who, if it hadn't been for his astronomical foresight, would be about as well-known as Popes John V, John VI and John VII. Gregory's mathematicians came up with a "not every four years" refinement; years divisible by 100 - but not 400 - contain a leap year. So, for instance, 1900 had no leap day, and neither will 2100. Slightly more complicated than the rhyme we all learn about "February has twenty-eight, but leap year coming one in four."(When the French had their 1st revolution and reformed their calendar by making it twelve months of exactly thirty days - with spiffy new names that owed nothing to Roman gods - they solved the leap year problem by adding on les jours complémentaires, a five or six day holiday. This seems extremely on point for a country that gave us both the metric system and naughty underwear.)
The most famous leap day custom is, of course, that of giving women the go-ahead to ask men for their hand in marriage. Known as Bachelor's Day in the UK and evidently spread haphazardly across Europe, it's gotten a bit confused in the US with Sadie Hawkins Day. Sadly, the transgressive thrill of dolls popping the question to guys has faded quite a bit in these modern times. Perhaps in the future, we can replace it with "Swipe Right Day," where everyone using dating apps has to okay whoever shows up in their timeline.
In a less secular vein, February 29 is also the feast day of St. Oswald of Worcester, a very nice early English bishop who keeled over on Leap Day 992, while washing the feet of the poor. For some reason, foot-washing hasn't caught on as an amusing leap year habit.Of course, the best thing about February 29th is its use as a plot point. There are a bunch of romances - usually historicals - featuring Bachelor's Day, and several YA novels about young people with once-every-four-years birthdays. And, my favorite, the idea that a leap year baby's chronological age doesn't line up with his birthdate is one of the key elements of the wonderful Pirates of Penzance. So let's go out to Rex Smith, Kevin Kline, and Angela Lansbury singing about a most amusing paradox... while rejoicing that this year gives us all one extra day for reading!
