The original account of Jesus riding on a donkey on Palm Sunday, in Mark 11:8-9, does not say that the people used palm leaves (NAB): "Many people spread their cloaks on the road, and others spread leafy branches that they had cut from the fields. And they that went before, and they that followed, cried, saying, Hosanna; Blessed be he that cometh in the name of the Lord."
The time of the Passover is too early for leafy branches (except palms), which the author of John's Gospel recognised, changing this reference to 'palm branches', thus creating our modern tradition of Palm Sunday.
John Shelby Spong (Jesus for the NonReligious) says that Mark's Gospel seems to have taken the reference to 'leafy branches' from the traditional Jewish observance of Sukkoth at an entirely different time of year:
The ]ewish eight day celebration of the harvest, known as Sukkoth, and also called the Festival of the Tabernacles or Booths, was probably the most popular holiday among the Jews in the first century. In the observance of Sukkoth, worshippers processed through Jerusalem and in the Temple, waving a bunch of leafy branches made of willow, myrtle and palm. As they waved these branches in that procession, the worshippers recited words from Psalm 118, the psalm normally used at Sukkoth. Among these words were "Save us, we beseech you, O Lord." Save us in Hebrew is hosianna or 'hosanna'. This is typically followed by "Blessed is the one who comes in the name of the Lord. (Psalm 118:25-6)."
The author of John's Gospel is known to have copied the account in Mark's Gospel, but amended this detail in order to make it more realistic. It is because of John's awareness and correction of the original error that we have palm leafs on Palm Sunday.
A:palms are used on palm Sunday to symbolize the palms that were laid on the ground for Jesus when he entered Jerusalem and after they are finished with the palms the burn them for the ashes for ash Wednesday
