The olive branch was the branch of the olive tree, which was regarded as a symbol of peace originating in ancient Greece.
In 2293, fleet admiral Bill described James T. Kirk as the Federation's first olive branch towards the Klingon Empire, when Kirk was ordered to escort Kronos One to Earth. (Star Trek VI: The Undiscovered Country)
In 2376, while trying to communicate with nucleogenic lifeforms, Chakotay described the crude message prepared as being a small olive branch, but an olive branch nonetheless. (VOY: "Equinox, Part II")
Later that year, The Doctor thanked Deanna Troi for extending an olive branch when she tried to mediate between him and Lewis Zimmerman. (VOY: "Life Line")