How does leap year work scientifically?

Answer 1

The earth doesn't go around the sun in an exact whole number of days. Over the centuries it took people a very long time to discover how to handle this (so that equinoxes, harvests, midsummer etc always come at the same date). The solution is to add a day every 4 years. Even that isn't exact, and this rule is not applied on certain occasions.

The rule, in the Gregorian calendar, is that years evenly divisible by 4 would be leap years, except that century years not evenly divisible by 400 would not be. This century year rule accounts for the small residual error of 3 days in 400 years that the original Julian calendar did not account for.

Answer 2

The average length of the tropical year is about 365.2422 days. Making 97 out of every 400 years one day longer than the usual 365 days makes the average length of the calendar year 365.2425 days.