Excerpted from the Handbook for Church Servers of Sergei Bulgakov:
On this day the Holy Church especially commemorates the imperial glorification of Jesus Christ before His death on the cross to indicate that the sufferings of the Savior were voluntary. The event of the feast is described in the Gospels (Mt. 21:1-11; Mark 11:1-11; Luke 19:29-41; John 12:12-19). The beginning of this feast goes back to deep antiquity. We meet the most ancient instruction on it in the teaching for this day of Methodius of Patara (3rd c.). Beginning from the VII century, many hymnographers (Andrew of Crete, Cosmas of Maium, John of Damascus, Theodore and Joseph of the Studite Monastery, the Emperor Leo the Philosopher, Theophanes and Nicephorus Xanthopoulos) have glorified the feast with hymns, which we sing even now. It is traditional to use palms on this feast (palm branches). It is even called "Palm" Sunday, "Flower bearing", "Flower offering" or "Flowery", and in popular usage "Palm Sunday". For us willows replace palms because the willow tree blossoms before other trees. The tradition to use palms on this feast is based on the circumstances of the event of the Entry of our Lord into Jerusalem. Praying as though we will invisibly meet the Lord and greet Him as the Victor over Hades and death, we hold in our hands the "signs of victory": the willows and lighted candles.
Troparion, tone 4
When we were buried with Thee in Baptism, O Christ God,
We were made worthy of eternal life by Thy Resurrection.
Now we praise Thee and sing:
Hosanna in the highest.
Blessed is He that comes in the name of the Lord.
Kontakion, tone 6
Sitting on Thy throne in heaven,
Carried on a foal on earth,
O Christ God.
And the songs of children, who sing:
Blessed is He that comes to recall Adam.
We magnify You,
O Christ the Giver of Life,
And we cry to You:
"Hosanna in the highest.
Blessed is He that comes in the name of the Lord."