Why do we have leap years? (an extra “leap day” in February every four years.)

The reason for leap years is to keep our current calendar in alignment with the astronomical solar years, which occur every time the Earth makes a full revolution around the sun.
Specifically, the actual solar year is 365 days, 5 hours, 48 minutes, and 46 seconds long. ( 365.2423 days in decimal terms.)
The rule for determining leap years is simply this: every year that is divisible by four is a leap year, except those that are divisible by 100 but not 400.
For practical purposes going forward, this means that leap years will occur every four years from now (2012, 2016, 2020, etc.) until we reach 2100, which will NOT be a leap year. However, because of the limitations of human life spans, it is unlikely that anyone reading this today will live long enough for this to be a concern. But if you do manage to survive until the end of the 21st century, just remember that February 2100 will only have 28 days.