The two most amusing explanations for why we have leap years that I’ve heard came from creationists:
Those scientists can’t even measure the length of the year accurately! They have to keep fudging their numbers every few years to make everything add up, so why should I trust them?
We have leap years because the earth is slowing down in its orbit, which proves that the earth can’t be old — a million years ago the earth would have been whirling around the sun so fast it would have flown out of orbit!
Phil’s detailed explanation isn’t quite as funny. My simple answer: the earth goes around the sun in 365 days plus a fraction. We carry the fraction each year until it adds up to one, and then we add a day to the year. We know with great precision how long a day is and how long a year is, and the adjustment is not to “fudge” the numbers, and we also know the rate at which both the day length is changing and the orbit is changing, and those numbers are miniscule and are not the reasons we have leap years.