Leap years exist because the solar year is approximately 365 and a quarter days long. Without a correction, the calendar would drift against the seasons by about six hours per year, accumulating to a full day every four years and a full month within a human lifetime. February receives the extra day because in the early Roman calendar it was one of the last months added and was assigned whatever days remained after the other months were filled. It has been the shortest month ever since. The leap year rule is not simply every four years: century years are skipped unless divisible by 400, which is why 1900 was not a leap year but 2000 was.
Daniel and Mom examine why the solar year is not a whole number of days, why February was left short in the Roman calendar, and why the leap year rule has a refinement that most people do not know about.

Daniel is nine. He asks the questions, refuses to accept easy answers, and picks every episode topic himself.

Mom does the digging - finding the sources, checking the claims, and translating them into something a nine-year-old will actually sit still for.
A leap year is needed because the solar year is about 365 and a quarter days, not a whole number.
Without correction the calendar would drift against the seasons by a day every four years.
February is shortest because it was added late to the Roman calendar and received the remaining days.
Century years skip the leap day unless divisible by 400. 1900 was not a leap year. 2000 was.
“I'm going to defend February for the rest of my life.”