bissextile adjective
referring to a leap year
bissextile noun
a leap year
bissext (also bissextus) noun
February 29^th, the extra day in a leap year

‘Let's leap for joy - today is Bissextile Day! ... Calm down, this story has nothing to do with gender preferences. Bissextile is the official name of the leap day we add every four years to keep our calendar in kilter.'
(The Virginian-Pilot, 29^th February 2004)

Contrary to what you might think, the word bissextile has nothing to do with issues of sexual orientation or gender! It refers simply to a leap year - a year containing February 29^th and therefore a total of 366 days. A noun derivative bissext refers to the extra day itself, though leap day is a common alternative in much wider use. February 29^th is often technically referred to as an intercalary day, intercalary being an adjective of Latin origin used to describe the insertion of an extra day in the calendar to harmonise it
A recent coining on the same topic is the countable noun leapling, used to refer to a person born on February 29^th. Twenty-first century leaplings can be united through a dedicated website, http://www.leapdaybabies.com/. A recent quote from the site states:

‘... Now you will always know someone born on the same day as you. If your child was born today, February 29, 2004 - Leap Year Day - Congratulations! Please register your little Leapling with us ...'

-ling is a suffix often used to imply that a person or thing is small or very young, as illustrated by words like duckling, seedling etc. In the same way, leapling is often reserved for a newborn leap day baby, also affectionately referred to as a leapy. The countable noun leaper is a slightly less recent general term for a person born on February 29^th. The website also humorously promotes a range of related terms, including an adjective leapless, which describes a person not born on February 29^th, and a noun leapship, which refers to a relationship between two people both born on a leap day.
 
Background
The word bissextile in fact has its origins in the sixteenth century, deriving from the Latin term bissextilis meaning ‘having an intercalary day'. In the Roman calendar, the sixth day before the ‘Calends of March' (i.e. 24^th February, counting back from the beginning of March) occurred twice in a leap year. Hence the term is based on Latin sextus - ‘six' - and bis - ‘twice' - and means ‘twice the sixth day'. The word bissextile is relatively rare in modern English, but emerges from obscurity every four years as illustrated by articles like the one cited above. The phrase année bissextile is however a commonly used French term for leap year.

The term leapling is a twenty-first century coining. The use of the word leap in reference to a year with 366 days dates from the time of late Middle English. In years with the extra day, feast days after February came two days rather than one day later than the previous year, and could therefore be said to have ‘leaped' a day.

From Macmillan English Dictionary