I have been around for about 17 of them. They typically don't faze me because I understand the nature of leap years in general.
The leap day is added to the calendar during Leap Years and turns the day into a 366 day entity in an effort to keep our calendar in alignment with the revolutions of the Earth around the Sun.
Were it not for Leap Days we would lose about 6 hours a year.
This equates to a loss of about 24 days a century. It would also screw up the equinoxes to a fair thee well.
If you were born on a Leap Day you are known as a 'Leapling'. I was not born on a leap day or in a leap year either for that matter.