The phrase "olive branch" is an idiomatic expression that means a gesture or action that signifies peace, reconciliation and goodwill. It refers to extending an offer of peace after a period of conflict or disagreement. The origin of the phrase comes from ancient Greek mythology where Athena, the goddess of wisdom, offered an olive branch as a symbol of peace after winning a battle against Poseidon for control over Athens.
The expression is often used figuratively to describe someone who tries to make amends or mend a relationship that has been damaged by conflict or misunderstanding. For example, if two friends have had an argument and one of them sends the other an olive branch as a sign of peace and reconciliation, it means they are trying to put their differences aside and rekindle their friendship.
In summary, "olive branch" is a phrase that conveys the idea of seeking peace and forgiveness after a period of discord or strife.