What are olive trees said to symbolize?

The Tree of Peace and Friendship. The phrase ‘extending an olive branch’ is commonly used when people try to make amends with each other. There are many references to olives throughout the bible, but this particular phrase originates from the story of Noah and the Ark. The tale tells about the 40 days and 40 nights of relentless rain and flooding. Once the storm had calmed, Noah sent a dove to find a sign of land. It returned with an olive branch in its beak, a sign that the worst was over. A glimmer of hope, peace, and a new start for humanity.

Source: Tree 2 My door