We just attended an institute class in which the symbolism of the palm leaf was explained.

At the time of the Savior's life, and indeed for centuries before that, a king would enter a city seated on a donkey as a symbol of peace.
That was opposed to an army entering on horses with the intent to conquer.

The palm leaf was waved as a symbol of victory.

So when the Savior entered on a donkey, he was telling the Jews that he was a king, and the waving of the palm fronds was symbolic of his victory, only not in a political sense.

This was very threatening to the Sadducees and the Pharisees, since they interpreted it as the end of life as they knew it ~ it was a threat to their livelihood.
And that's why they wanted Jesus crucified.