12 The next day a great multitude that had come to the feast, when they heard that Jesus was coming to Jerusalem,
13 took branches of palm trees and went out to meet Him, and cried out: “Hosanna! Blessed is He who comes in the name of the LORD!’ The King of Israel!”
14 Then Jesus, when He had found a young donkey, sat on it; as it is written:
15 “Fear not, daughter of Zion; behold, your King is coming, sitting on a donkey’s colt.”
16 His disciples did not understand these things at first; but when Jesus was glorified, then they remembered that these things were written about Him and that they had done these things to Him.
17 Therefore the people, who were with Him when He called Lazarus out of his tomb and raised him from the dead, bore witness.
18 For this reason the people also met Him, because they heard that He had done this sign.
19 The Pharisees therefore said among themselves, “You see that you are accomplishing nothing. Look, the world has gone after Him!”
In John 6:15, the Jews wanted Jesus make King by force, but it wasn't His hour. Now He presents Himself as King to fulfill Zechariah's prophecy.
Zechariah 9:9-11 — “Rejoice greatly, O daughter of Zion! Shout, O daughter of Jerusalem! Behold, your King is coming to you; He is just and having salvation, lowly and riding on a donkey, a colt, the foal of a donkey. I will cut off the chariot from Ephraim and the horse from Jerusalem; the battle bow shall be cut off. He shall speak peace to the nations; His dominion shall be ‘from sea to sea, and from the River to the ends of the earth.’“As for you also, because of the blood of your covenant, I will set your prisoners free from the waterless pit. This prophecy was partly fulfilled at this time. The remainder will be fulfilled at His second coming.
The crowd had heard about His miracle with Lazarus and rushed to see Him (v. 13). Josephus estimates the Passover crown in Jerusalem to be about three million people.
Palm branches (v. 13) symbolize victory. They were waved for kings and generals (Revelation 7:9). They will also be found in the Millennial temple (Ezekiel 40:31).
Hosanna! (v. 13) = Save Now! (Psalm 1188:20-27; Zephaniah 3:15; John 1:49)
There is no record that Jesus responded to the crowd in any way.
donkey (v. 14) — a symbol of humility (Matthew 21:7; Luke 19:29-35). He came meekly. The Romans could not see Him as a threat to Caesar. At His second coming, He will ride a horse (Revelation 19:11).
He who came before in humiliation and shame shall return in power and majesty. He who once had not where to lay His head shall then sit on the throne of His glory (Matthew 25:31). He who was nailed to a malefactor's cross shall, in that day, wield the sceptre of imperial dominion. Just as the "ass" was well suited to the One who had laid aside His glory, so the white "war-horse" of Revelation 19 is in perfect keeping with the fact that He is now "crowned with glory and honor." — Expositon of the Gospel of John, by Arthur W. Pin, page 257.
His disciples did not understand (v. 16) until after the resurrection when Jesus was glorified (John 14:26), after the Spirit came on them at Pentecost. The believed, but they didn't understand.
The Pharisees (v. 19) had tried to turn the people against Jesus, but hadn't been able to — yet. The people thought Jesus would be a victorious King who would defeat the Romans and restore the kingdom. When He didn't, four days later the same people shouted, "Crucify Him!"
This event took place exactly on the day of the completion of Daniel's 69th week. It also fulfilled prophecies of Genesis 49:9-11; Daniel 9:24-27.
Jesus fulfilled these obvious prophecies and presented Himself publically so there could be no doubt who He was. All their excuses for rejecting Him were gone.