It is a list of the names of Curetes and Vestia Nuns who took a duty in Prytaneon. Curetes and the Vestal Virgins were in charge with the eternal flame, which was symbolizing the existence of the city.
Vestal Virgins who were priestess and were named after goddess Hestia (or Vestia) who was in charge with Household and the flame. There are two re-erected Doric columns at the Prytanion. On each piece of marble there were the names of Curetes and Vestal Virgins who were in charge to keep eternal flame.