Leap years contain an extra day in February: 29 days instead of the usual 28. Every year divisible by four is a leap year -- unless it's divisible by 100, in which case it's not, unless it's also divisible by 400, in which case it is. Got it?
The purpose of a leap year is to align the calendar year with the astronomical year. While the calendar year holds 365 days, it actually takes the earth 365.2422 days to revolve around the sun. This extra six hours a year can add up -- if we didn't have leap years, we'd be out of sync by 28 days every 100 years.
So summer would eventually creep into fall, and eventually winter, and so on. For us in the Northern Hemisphere, it would be very strange to have short, frigid days in July. The Romans realized this, which is why they decreed the first leap year in 46 B.C.
However, adding an extra day every four years is actually too much of a correction (hence the need for the rules about being divisible by 400 versus 100). No calendar is perfect, but the Gregorian seems to work fairly well.