How often and why is there a leap year?

The year isn't exact; instead of being 365 days, it is 365.26 days.

The Gregorian calendar uses leap years to keep the calendar in synchronization with the seasons. Many religions, including Jews and Christians, expect certain holidays to occur in specific seasons. For example, Easter and Passover are spring holidays (living in the northern hemisphere, as most people did back then) with Christmas in the winter.

The old Julian calendar didn't do that, and by the 1500s, the date of Easter was two weeks out of whack. So Pope Gregory organized a commission to revise the old calendar, and in 1582, the new calendar was adopted. So we have a leap year in any year that is divisible by four or 400, but not century years otherwise.