In ancient Rome, February 24 was doubled making it 48 hours long, in the same way that February 28 is doubled every four years in the modern calendar, except we call it a different day.

All leap days and years are attempts to to align a calendar, which is based on whole days and the orbit of the Earth around the Sun, which cannot be nicely divided into 24-hour days.

Using a purely day-based calendar, Earth’s exact position in its orbit around the Sun would change slightly in date each year. To make up for this slight difference Ancient Rome doubled every February 24.

February 24 is also the date of the annual regifugium or Flight of the King. In 510 BC. In his Fasti, Ovid offers the longest surviving account of the observance:

Now I must tell of the flight of the King, six days from the end of the month. The last of the Tarquins possessed the Roman nation, an unjust man, but nevertheless strong in war.

Summarized from Wikipedia and The Roman Calendar and the Regifugium.