When the disciples had untied it [the young donkey] and brought it to Him, then He found it and sat thereon.
In doing so He fulfilled the prophecy of Zechariah who said “Fear not, daughter of Zion: behold, thy King cometh to thee, sitting on the colt of an ass” (see Zech. 9:9).
Because most of the kings of Jerusalem were wicked and tyrannical, the prophet said, “Fear not, O Zion. The king of whom I prophesy to you will not be like the others, but meek and humble, displaying no arrogance whatsoever.”
This is shown by the fact that He came seated upon an ass. He did not enter the city at the head of an army, but conveyed by a donkey.
His sitting upon an ass was also a symbol of things to come.
Being unclean according to the law, the ass represents the uncleanliness of the Gentile race, upon whom Jesus, the Word of God, sits, subduing like a colt this insubordinate and uninstructed people, this new race, and leading it into the true Jerusalem once it has been tamed and made obedient to Him.
Has the Lord not gathered the Gentiles into heaven, once they became His people and were obedient to His preaching?
As for the palms, do they not indicate perhaps that He Who raised Lazarus has become the Victor over death? For palms were awarded to those who were victorious in games and contests.
Perhaps they also indicate that He Who is being praised is a heavenly Being Who has come from above.
Of all trees it is the palm that appears to soar upwards to the very heavens, so to speak; it bears foliage at the top, and at the peak puts out young white shoots, but the stump and the middle section of the trunk, all the way to top, are rough and hard to climb because of the sharp spines.
So it is that he who strives to acquire knowledge of the Son and Word of God will find it a hard and uphill journey because of the toil of gaining virtue.
But when he has arrived at the pinnacle of knowledge, he will be met, as if by the whitest palm shoots, by the bright light of divine knowledge and the revelation of ineffable things.
[…] These things understood not His disciples at the first: but when Jesus was glorified. By glory he means the Lord’s Ascension after the Cross and Passion. Only then, by the coming of the Holy Spirit, did they understand that these things were written of Him.
Theophylact of Ohrid (1055-1107): Explanation of the Gospel of St John, on John 12:14-16 @ Chrysostom Press.