This year, 2016, is a leap year in the Gregorian calendar, so we had an extra day inserted last month. It is usually thought that this day is inserted at the end of the month, since the last day is the 29th day of February. However, the leap day is actually inserted on the 24th day! Let me explain...
In the Gregorian calendar, as in the Julian calendar, days were originally not counted forward from the beginning of the current month, but backwards from the beginning of the next month. (Or from a couple of other fixed days, such as the Ides of March coming up in three days.) Thus, the extra day was added as the sixth day from the Calends of March. The Calends is the first day of the month and was counted as the first (i) of the Calends, while the last day of the previous month was counted as the second (ii), and so on, so the last day of February (the 28th in most years) was the 2nd day of the Calends of March, even in leap years. The extra day was added to the sixth (vi) day of the Calends of March, which is the 24th day of February, for religious reasons. And instead of adding a number, e.g. ...7, 6, 5..., they gave the extra day the same number, i.e. ...7, 6, 6, 5..., so that there were two days named the sixth day of Calends, the 24th and 25th. Apparently the first (24) or second (25) were considered the extra day in different periods, but it hardly matters, because they were treated like one 48-hour day. Because there were two sixth days, leap years were called "bissextile", from the Latin bis sextum, meaning "two sixes".
Unlike the current practice, where those born on the extra day are denied birthdays three out of four years, those born on that day celebrated on the 6th Calends every year, which is the 24th in our modern reckoning. Those with birthdays after that celebrated one day later by our count, so if you were born on the 29th (the day before Calends) then you celebrated on the last day of February every year, because it was always the day before Calends. Likewise, those born on the 26th day in a leap year would celebrate on the 25th in ordinary years, because it was the 5th of Calends. Those born before the extra day were not affected. Other dates, especially religious holidays, were treated the same way. For instance, the 24th day of February was traditionally the Feast of St. Matthias, except in leap years it was the 25th. The Catholic Church has kept this practice up to modern times, although it may now be changing.