In antiquity palm leaves were used to signify victory, especially military triumph, and were bestowed upon the illustrious by personifications of Victory or Fame.
Christianity adopted the palm for martyrs who had triumphed over death. During the Flight into Egypt the fruit of the palm tree fed Joseph and the Virgin, who is shown at her death being presented with a palm. The palm is also associated with Christ's Entry into Jerusalem, when the people "took branches of palm trees, and went forth to meet Him, and cried Hosanna: 'Blessed is the King of Israel that cometh in the name of the Lord'". This event is remembered in the Christian celebration of Palm Sunday.
Question and answer were taken from page 166 of The Dictionary of Symbols in Western Art by Sarah Carr-Gomm. The book was published by Facts on File in 1995.