Why is this day called Palm Sunday?
In memory of our Saviour's triumphant entry into Jerusalem, when the multitude strewed palm branches before Him, for which reason the Church, on this day, blesses palms, and carries them in procession.
Why are palms blessed?
That those who carry them with devotion, or keep them in their houses, may receive protection of soul and body, as prayed for in the blessing; that those who carry the palms may, by means of the prayers of the Church, adorn their souls with good works and thus, in spirit, meet the Saviour; that, through Christ whose members we are, we may conquer the kingdom of death and darkness, and be made worthy to share in His glorious resurrection and triumphant entrance into heaven.
St. Augustine writes of the palms: “They are the emblem of praise, and sign of victory, because the Lord by death conquered death, and with the sign of victory, the cross, overcame the devil, the prince of death."
Therefore, preceded by the cross, we go in procession around the church singing hymns of praise; when we come to the church door, we find it locked; the priest knocks at it with the cross. Heaven was closed to us by the sin of Adam, and it is opened to us by reconciliation through Jesus on the cross.
From "The Church's Year" by Fr. Leonard Goffine