In Greek mythology, the Olive tree was a gift from the Gods to humans. The story goes that a competition took place between the Goddess Athena and Poseidon, God of the Seas. Whoever would give the best gift to the city of Athens would win.
Poseidon went first and strook the rock of Acropolis with his trident and and created a salt water lake. Athena followed and where her spear hit the rock an Olive Tree appeared and immediately started bearing fruit.
The olive was of course judged to be the better gift ! The city was named in Athena's honour and the Olive Tree on the Acropolis became the symbol of the city.