Hestia was the daughter of Cronus and Rhea. She was the goddess of Fire in its first application to the wants of mankind, hence she was essentially the presiding deity of the domestic hearth and the guardian spirit of man, and it was her pure and benign influence which was supposed to protect the sanctity of domestic life.
Now in these early ages the hearth was regarded as the most important and most sacred portion of the dwelling, probably because the protection of the fire was an important consideration, for if once permitted to become extinct, re-ignition was attended with extreme difficulty. In fact, the hearth was held so sacred that it constituted the sanctum of the family, for which reason it was always erected in the centre of every house. It was a few feet in height and was built of stone; the fire was placed on the top of it, and served the double purpose of preparing the daily meals, and consuming the family sacrifices. Round this domestic hearth or altar were gathered the various members of the family, the head of the house occupying the place of honour nearest the hearth.
Here prayers were said and sacrifices offered, and here also every kind and loving feeling was fostered, which even extended to the hunted and guilty stranger, who, if he once succeeded in touching this sacred altar, was safe from pursuit and punishment, and was henceforth placed under the protection of the family. Any crime committed within the sacred precincts of the domestic hearth was invariably visited by death. In Grecian cities there was a common hall, called the Prytaneum, in which the members of the government had their meals at the expense of the state, and here too was the Hestia, or public hearth, with its fire, by means of which those meals were prepared.
It was customary for emigrants to take with them a portion of this sacred fire, which they jealously guarded and brought with them to their new home, where it served as a connecting link between the young Greek colony and the mother country. Hestia is generally represented standing, and in accordance with the dignity and sanctity of her character, always appears fully draped. Her countenance is distinguished by a serene gravity of expression.
Vesta occupies a distinguished place among the earlier divinities of the Romans. Her temple in Rome, containing as it were the hearthstone of the nation, stood close beside the palace of Numa Pompilius. On her altar burned the never-ceasing fire, which was tended by her priestesses, the Vestal Virgins. The temple of Vesta was circular in form, and contained that sacred and highly prized treasure the Palladium of Troy. The great festival in honour of Vesta, called the Vestalia, was celebrated on the 9th of June.
From: Berens, E.M. The Myths and Legends of Ancient Greece and Rome. New York: Maynard, Merril, & Co., 1880. Text in the public domain.