Hestia is the anglicised version of her name. Her Greek name - Εστία (pronounced es-tee-ah) - means dwelling. She was the goddess of home, and goddess of the hearth. On Olympus, her job was to take the good stuff from every sacrifice, to any deity, and feed it into the fire on the mountain. And so, part of every sacrifice belonged to her. Every hearth-fire belonged to her too. And, in those days, there were hearth-fires everywhere: in every home, every temple, even up on Mount Olympus.
Olives, the olive branch and the olive tree are symbolic in many cultures and religions, from ancient Egypt to Christianity to the Arab world. In ancient Greece, newborn babies were presented with an olive branch, brides wore a crown of olive leaves, and olive wreaths were given to the dead. It was illegal to cause damage to an olive tree in ancient Greece - a crime that was actually punishable by death at one point! The olive tree was also sacred to Athena and had a special place in the myth of the founding of Athens, the city I live in.