There are a few ideas that the palm tree represents in Judaism - I am not sure that any one reason is more symbolic than any other one.
(i) The palm tree is the tree under which the Prophetess Deborah sat and judged the Jewish People.
(ii) It is one of the seven species of fruit that are praises of the Land of Israel.
(iii) Psalm 92 compares the righteous people to a palm tree, "The righteous shall flourish like a palm tree"
(iv) The palm tree was a symbol of Judea.
