Occurs in years that are evenly divisible by 4, such as 2012 and 2016, unless the year is also divisible by 100 with the exception that years evenly divisible by 400 are leap years. So 1900 was not a leap year (multiple of 100) but 2000 was a leap year (multiple of 400).
The Julian calendar established in ancient Rome applied a leap day every 4 years, always. This over compensated by a tiny amount that accumulated over the centuries. By 1582 (395 leap years since 1 AD) the calendar had shifted by 10 days and Pope Gregory XIII decreed the new calendar rules described above and moved the calendar 10 days forward to correct for errors since the birth of Christ.
What happens if you're born on a Leap Day? In the comic opera, The Pirates of Penzance, Frederic celebrates his 21st birthday and his release from apprenticeship to a band of kind-hearted pirates. Or so he thinks. He learns that he was born on a leap day with a birthday only every 4 years and won't be 21 for another 63 years.
In reality the UK recognizes March 1 as the birth date in non-leap years for someone born on Feb 29.
For the super picky, there is also a Leap Second. Every few years astronomers add 1 second to atomic clocks to keep them 100% on track with the sun. Normal clocks ignore the extra second.