February 29 is a date that occurs only every four years, in years evenly divisible by 4, such as 1988, 1996, 2008 or 2016 (with the exception of century years not divisible by 400, such as 1900) for the Gregorian calendar, which is most widely used in the world today.
Got all that? OK then 
The Gregorian calendar is a modification of the Julian calendar first used by the Romans. The Roman calendar originated as a lunisolar calendar and named many of its days after the syzygies (Love that word!) of the moon: the new moon (Kalendae or calends, hence “calendar”) and the full moon (Idus or ides).
However,
…some exceptions to this rule are required since the duration of a solar year is slightly less than 365.25 days. Years which are evenly divisible by 100 are not leap years, unless they are also evenly divisible by 400, in which case they are leap years. For example, 1600 and 2000 were leap years, but 1700, 1800 and 1900 were not. Going forward, 2100, 2200, 2300, 2500, 2600, 2700, 2900, and 3000 will not be leap years, but 2400 and 2800 will be. By this rule, the average number of days per year will be 365 + 1/4 − 1/100 + 1/400 = 365.2425, which is 365 days, 5 hours, 49 minutes, and 12 seconds.
Yeahhhhhhh….but….um…
A leap year is also known as an intercalary year.
Folk Traditions:
In the English speaking world, it is a tradition that women may propose marriage only on leap years.
And for all you math geeks, they even have an algorithm for it!
if year modulo 400 is 0 then leap
else if year modulo 100 is 0 then no_leap
else if year modulo 4 is 0 then leap
else no_leap
The Revised Julian calendar adds an extra day to February in years divisible by four, except for years divisible by 100 that do not leave a remainder of 200 or 600 when divided by 900. This rule agrees with the rule for the Gregorian calendar until 2799. The first year that dates in the Revised Julian calendar will not agree with those in the Gregorian calendar will be 2800, because it will be a leap year in the Gregorian calendar but not in the Revised Julian calendar.
Who cares? I'll be dead!
The Gregorian calendar was designed to keep the vernal equinox on or close to March 21, so that the date of Easter (celebrated on the Sunday after the 14th day of the Moon that falls on or after 21 March) remains correct with respect to the vernal equinox.
Last year the Vernal Equinox was on March 21st, this year it will be on March 20th...
The vernal equinox year is about 365.242374 days long (and increasing), whereas the average year length of the Gregorian calendar is 365.2425.
Details, details...
A person born on February 29 may be called a "leapling". In common years they usually celebrate their birthdays on 28 February or 1 March.
"Leapling"...Isn't that what Inga (Teri Garr) calls Dr Fonkensteen (Gene Wilder) in Young Frankenstein?
For legal purposes, their legal birthdays depend on how different laws count time intervals. In Taiwan, for example, the legal birthday of a leapling is 28 February in common years, so a Taiwanese leapling born on February 29, 1980 would have legally reached 18 years old on February 28, 1998.
If a period fixed by weeks, months, and years does not commence from the beginning of a week, month, or year, it ends with the ending of the day which proceeds the day of the last week, month, or year which corresponds to that on which it began to commence. But if there is no corresponding day in the last month, the period ends with the ending of the last day of the last month.
HUH???
And Lastly, Zeller's congruence:
Zeller's congruence is an algorithm devised by Christian Zeller to calculate the day of the week for any Julian or Gregorian calendar date.
Formula:
For the Gregorian calendar, Zeller's congruence is

for the Julian calendar it is

where
 h is the day of the week (0 = Saturday, 1 = Sunday, 2 = Monday, ...)
 q is the day of the month
 m is the month (1 = January, 2 = February, 3 = March, ...)
 J is the century (actually )
 K the year of the century ().
January and February are counted as months 13 and 14 of the previous year.
And especially for my friend Brian, whose website makes me feel dumb:
Implementation in software:
The formulas rely on the mathematician's definition of modulo division, which means that −2 mod 7 is equal to positive 5. Unfortunately, the way most computer languages implement the remainder function, −2 mod 7 returns a result of 2. So, to implement Zeller's congruence on a computer, the formulas should be altered slightly to ensure a positive numerator. The simplest way to do this is to replace − 2J by + 5J and − J by + 6J. So the formulas become:

for the Gregorian calendar, and

for the Julian calendar
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