The procession of Jesus on a donkey was at once symbolic of his being, like Solomon, the son of David, of his being Judge and Ruler over Israel, like the seventy sons and nephews of Abdon, and of his humility: a donkey is not a proud beast. This betokens his willingness to suffer for us and for our sins.
Today we read the Gospel differently: a reader reading the narrator's parts, the celebrant reading Jesus' parts, and the parts of the various people speaking read by the congregation. An excerpt of that is here.
The sermon is here.