From Tolkien Gateway

Overlithe was the leap day of the Shire Calendar. It was added as an extra day every four years to accommodate annual deficits between a 365-day calendar and the actual length of a year (which is a little under a quarter of a day longer) except when this year was the last of the century.

Overlithe occurred between Mid-year's Day and the second of the two normal Lithedays (2 Lithe). It had no weekday name, and was treated as a special holiday by the inhabitants of the Shire.

A leap year was S.R. 1420, and on that Overlithe there was the greatest merrymaking, because of its plentifous harvest and wonderful summer.[1]