Why is Athena represented by the olive branch?

Actually, this is a very long story, so I will shorten it up for you. :)

Poseidon and Athena wanted to be patrons for the city of Athens. The king at that time decided that the god that would bring the best gift to the city would win. Poseidon made a salt-water spring. Athena made an olive tree, which was really useful, for olive oil and food.

Athena won and she is now represented by the owl and the olive branch. The olive branch stands for peace. I really hope this helped. :)