What makes it so important? It is the message Jesus is sending, which is often misunderstood and too often taught incorrectly.
The story has Jesus riding a donkey into Jerusalem. The Jesus' followers and even the crowds began cheering. They were offering up the interwoven spiritual and nationalistic cheers for this donkey riding rabbi. Luke has the Pharisees telling Jesus to quiet the crowds to which Jesus responds that even if he did, the stones would cry out.
So what's happening? Let's put the story into the context in which it occurred. First, we must remember that Jesus is Jewish. Jerusalem's people are Jewish. The religious leaders are Jewish. So it strikes me that we should look at this event through Jewish eyes to understand it (which most do not ironically).
The first mistake people make is the very reason Jesus is riding a donkey. Jesus rides the donkey NOT to be humble. On the contrary, he rides the donkey to elicit praise and adoration. From the O.T. tradition, the kings of Israel rode donkeys. Yes, Zechariah has a verse about riding the donkey in humility, but the very image of the donkey is one of kingship. So, when Jesus rides a donkey into Jerusalem, he is in fact making a startling claim: He is King and worthy of praise.
The second mistake is what this does to the crowds. They are not worshiping Jesus as the Son of God. They are adoring a challenger to Rome. In Jesus (or anyone willing to lead them), the Jews saw a possibility of overthrowing the Romans. As this young, popular leader takes the mantle of leadership/kingship by riding the donkey, the people cheer for they want the oppression, the taxation, and the humiliation of Roman occupation to end. The crowds are cheering a hero-to-be. They want a military coup, and symbolized by donkey, Jesus is a tantalizing possibility.
The third mistake is continues this same theme. The Pharisees are not asking Jesus to avoid being adored. They are begging Jesus to not rouse the attention and anger of the Romans. Potential Messiahs had come and gone...each leading failed rebellions against the Romans, and each one leaving the Jewish people in a worse position as the Roman military tightened the vice on Palestine. This is, from a historical perspective, the reason why Jesus is crucified. He was a threat to Rome. The Jewish leaders were quick to hand him over to the Romans as a peace offering. What an irony for that is exactly what he was.
What is at stake in this scene is the Kingship of Jesus. Notice that this is all the Romans are concerned with during the trial and crucifixion: "Are you the King of the Jews?"
Jesus riding the donkey made that claim, and the people spread their palms out before him. Yet, just a few days later those same people were apathetic or fleeing or even condemning Jesus to death.
I cannot hold a palm on Palm Sunday without thinking of Ash Wednesday for I see in the palm waving in my hand the sin and betrayal of Jesus I have and will commit even while I wave it in worship of Him. The tension of the Sunday is hard to hold, and maybe it helps us understand the Grace we live with...for every day we worship Jesus we also end up betraying him. It's nothing new.