A week before Easter Sunday, the day of the Resurrection, Jesus rode into Jerusalem. This marked the beginning of the end, and he knew that he was riding towards his own death, which had been foretold in the scriptures.
Jesus chose to enter the city on a donkey, which he ordered his disciples to borrow for the purpose. Actually, it’s a little unclear what he was riding on, because he sent the disciples to collect an ass and a colt, which they did, and “set him thereon” – well, thereon being which: both of them? Anyway, this neatly allowed him to fulfil the prophecy towards the very end of the Old Testament: “Behold, thy King cometh unto thee: he is just, and having salvation; lowly, and riding upon an ass, and upon a colt the foal of an ass.” (Zechariah 9, 9).
As he rode, the people spread their clothes in the road, and cut down branches from the trees, and strew them in the way (or strawed them in the way, as the lovely King James Bible has it).
So this is the origin of Palm Sunday; presumably the trees that lined the road into Jerusalem were palm trees, and that is why we hold palm crosses in church on Palm Sunday, to commemorate Jesus’ final entry into the city. And you will remember, of course, that it is these palm crosses that get burnt to create the ash for Ash Wednesday.