"Olive branch" and "dove of peace" are generally considered as symbols of peace.
Speaking of a country "extending an olive branch", it is generally described as expressing a friendly attitude and a desire for peaceful and win-win development for this country.
For an individual, "extending an olive branch" means showing kindness to someone and giving someone a chance. For example, sometimes you will see a recruitment company offering an olive branch to someone, and you want to hire him.
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Tracing back to the source, we must start with the fairy tale of Noah's Ark in the Bible. One day in ancient times, God found that except for the Noah family, the moral consciousness of human beings was getting worse and worse, almost to the point of hopeless. So, I decided to use the flood to engulf all mankind except Noah. God informed Noah and his wife in advance to prepare a square wooden boat with enough dry food and water, and selected a pair of various animals to take on board.
Then the flood came, and all the creatures in the world failed to escape this disaster. Only Noah's Ark drifted safely. After a long time, the flood receded and mountains, islands and open spaces appeared in the distance. Noah and his wife are very happy. First, they released a pair of pigeons from the boat into the blue sky and set them free.
But not long after, the pigeon flew back again, holding a emerald olive branch in his hand, which seemed to convey a message: the earth is back to life and everything is peaceful! Since then, the olive branch has become synonymous with "peace", and pigeons are also called "messengers of peace" and "doves of peace".
Nowadays, in the communication of some countries, there are always scenes of waving olive branches or flying pigeons for peace. The symbol of the United Nations is also a pair of olive branches supporting the earth.