This year the child of one of my good friends will be celebrating his birthday on his actual birthday for only the third time. Why is this? He was born on February 29, of course.
Why is George Washington's birthday recorded as both February 11, 1731 and February 22, 1732? It's recorded as both because of the change from the Julian Calendar to the Gregorian Calendar in 1752 (read more about Washington's birthday on Archives.gov).
Here are a couple of videos that explain the history of our modern calendar and why we have an extra day every four years.
This video was shot on February 29, 2008 which is why you here the narrator say "today is leap year." Four years later it is still a good, brief explanation of leap year.
And while we're on the topic of time, here are a couple of videos about daylight saving time.
H/T to Brain Pickings for the first video.