Piccolo Day is held on May 9th. This is the day that King Piccolo declares his ruling of Earth in "Tenshinhan's Resolve" and "Prelude To Vengeance". In the FUNimation Dub, this date was localized to the 13th to keep the association with bad luck (9 being an unlucky number in Japanese culture).
King Piccolo says that he will take a slip from the box (being held by his son, Piano) each year on the Piccolo Day, and the chosen sector on the slip will host that year's celebration and will end in its destruction at the hands of King Piccolo himself.
The ceremony is celebrated by King Piccolo once, in Age 753. The only sector chosen among the 43 sectors on Earth is sector 28, the location of West City. However, the city is not destroyed due to Goku killing King Piccolo on this day before the latter leaved Central City.