Symbolism: In Antiquity

Athena was not always the Goddess of Athens. She competed with Poseidon for the position. Both Gods offered the people of Athens gifts. Poseidon gave them a salt spring. Athena gave them the olive. The Athenians chose Athena. This is said to be the reason there is always an olive tree at the Acropolis.

Source:

After the founders of Rome, Romulus and Remus were left for dead by their parents they were said to have been found under an olive tree by a wolf.