John 12:12-13.
On the next day much people that were come to the feast, when they heard that Jesus was coming to Jerusalem,
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.

There were throngs of people in Jerusalem for this most important feast day of the year, the Passover. And with the people, there were sheep. Jewish law demanded that the sacrificial lamb live with the family for at least three days before the feast. That’s partly why so many people came early. They had to purchase a lamb, and stay in Jerusalem or nearby before the day of the Passover. The historian Josephus tells us that someone counted, at some point, over 265,000 lambs coming into the city. All those lambs, and the Lamb of God among them.
I’ve never been to Jerusalem. Friends who have been there tell me it’s not as big as they expected (not the older part) and that it’s typically crowded on a normal day. Think of thousands coming from all over Israel, especially from Galilee, and filling every available spot in the city. Noise, confusion, children running here and there, people hawking food, lambs, and many other items for sale; even in the Temple, lambs were being sold. Add to all that the occasional clatter of hooves when Roman soldiers rode through, sending people running to get out of the way.
It couldn’t have smelled very good, either. Horses, sheep, donkeys–all leaving smelly reminders behind them.
And what about the palm branches? Why were they used?
Palm leaves and branches had been a symbol of Jewish nationalism since the days of the Maccabees. You can read about them here. The people saw Jesus more as a political figure, a king, than as the perfect Lamb of God Who was sent to give His life for their salvation.
So they welcomed Him with great joy and celebration as He entered the city on a donkey selected for just that purpose. Hosanna means save us now. It is clear that the people were hoping for freedom from Rome, and that such freedom would be claimed under the leadership of Jesus. He was immensely popular with the common people who, even after seeing His miracles and hearing Him teach, still didn’t get it. They wanted a king to set them free from Rome, and they thought Jesus was the one who would do that for them.