The olive tree has an ancient history with mythologies and traditions.
Mythologies
The olive tree is deeply associated to Athena, the Goddess of wisdom and strategist of warfare. Glaukopis is her nickname given by Homer. She is like a bright-eyed, night-sighted owl with her wisdom which is why you may often see her image with a small owl perched atop her head.

Pallas Athena

Athena has another name: Pallas Athena. During the War of the Giants, Athena accidentally killed Pallas. She was distraught from his death and wanted to honour him by placing his name before hers.

Athena and the God of the sea and earthquakes, Poseidon, were competing over who should become the celestial benefactor of Attica. This competition was created by Zeus. The "Athenians" were to be given the winner of this competition as a gift.

The competition went like this: Poseidon took a Trident and beat the earth till water shot up from the ground. The salty water did not taste good, nor did it do any good to the Athenians.

Athena, on the other hand, hit the ground on a hill, called Acropolis, with her spear. A beautiful full-grown olive tree with ripe olives appeared.

This olive tree had many uses:
1. The olives were delicious to eat
2. The olives, when pressed, produced a good oil
3. The tree was wood

They viewed this as a Divine gift.
Pallas Athena’s benefactor represented peace and wisdom. The olive tree from that time onward equates with the most sacred of qualities.
A comparable myth exists in the Greek and Roman mythology that Poseidon presented the first horse as the gift. Again, the Athenians chose the olive tree. Athena won the contest. There were major differences between the two gifts. Athena's gift embodied peace. The horse embodied war.
Athens, Greece was so named for Athena because she was a Goddess. The Parthenon was her shrine.
An olive wreath crowns her helmet; the amphorae of her statue further identifies her role with the olive tree and olive oil.
The olive tree was the ancient logo symbol of the Olympic Games. In 776 BC the very first Olympic torch was lit from an olive branch.

The farming God was Aristeos, he initiated the cultivation and care procedures for the olive trees. The myth states that he created mills to help with the extraction of the olive oil. The olive trees were long living and greatly enhanced the economy. The trees represented significant prosperity.
Hercules
Hercules so named by the Romans was also known as Heracles the God of victory and commerce. Hercules planted the precious olive tree on Mount Olympia. This tree produced the olive leaf crown made by King Iphitos (Hercules descendant) to go on the head of the Olympic game winners. These crowns bestowed mystical powers to the owner and represented victorious honour.
The olive oil merchants of Ancient Rome dedicated the round Temple of Hercules Olivarius, to Hercules. This is in the Forum Boarium. People call it the Temple of Vesta, which is wrong.
The Traditions of the Ancient Olive Tree
Olive trees date way back to even Biblical times. The olive oil mixed with balsam was used as a sanctity anointment for royalty and hallowed dignitaries. This olive oil / balsam blend is called Chrism. This anointment is used in blessings and Christenings; even today it’s used in this manner. The oil was dropped into saints’ graves. The winning Greek athletes were also anointed with it.