Traditionally, the olive branch has been used as a symbol of peace. Its origins as a symbol of peace come from ancient Greek culture, when Athena planted an olive tree to win possession of Athens over Poseidon. Since then it has been used throughout many different cultures around the world.
The olive branch also has connections to the Roman empire. During that time, when a leader held out an olive branch, it was considered a signal of pleading for peace. Additionally, the olive branch is related to Christianity as well. As told in the Bible, after the flood, Noah sent a dove out to search for dry land and the dove returned to him bearing a leaf from an olive tree. The olive tree leaf was meant as a sign to Noah that God had ceased His war on mankind and the water was beginning to recede.
It is not fully known why the olive branch, or the olive tree for that matter, is associated with peace. It is thought that the association might originate from the fact that olive trees take a very long time to grow, which led farmers to not grow them during times of war. If farmers were planting olive trees, it meant that there was peace and ample time for growing, so olive trees became associated with peace time.
The olive branch has also been used frequently in the imagery of American politics, with the Great Seal depicting a bald eagle with arrows in one talon and an olive branch in another. This is meant to signify the powers of war and peace, which are exclusively granted to Congress, the American government's law-making body.