Blessed is He who comes in the name of the Lord!
Blessed is the coming kingdom of our father David!
Hosanna in the highest!"
-Mark 11:9, 10
With this joyous proclamation of salvation, the citizens of Jerusalem mark the entry of Jesus into the city. Quoting Psalm 118:26, they shout out that Jesus "comes in the name of the Lord". Psalm 118 is a psalm written in honor of God's saving grace. It reminds us that the Love of God endures forever (v. 1), the God answers our prayers and sets us free (v. 5), and that the rejected stone will become the capstone (v. 22 and brought up by Jesus after his entry into Jerusalem - Mt 21:42; Mk 12:10,11; Lk 19:17).
The return of the Davidic line of kings is also praised. As I've brought up a few times, one of the major views n the Messiah is that He would be a Davidic king ushering in a new age for the people of Israel (see: Jewish Views On the Messiah). Jesus reinforces this idea by riding in on a donkey. In verse 22:5, Matthew reminds us that the prophet Zechariah says, "Say to the Daughter of Zion, 'See, your King comes to you, gentle and riding on a donkey, on a colt, the foal of a donkey,'" (Zec 9:9). When David named Solomon king over Israel, he had his officials place the boy on a donkey and marched through the streets proclaiming the anointing of the royal son (1Ki 1:32-40; keep in mind that Jesus was anointed at some point during Holy Week and Solomon shortly after his royal procession). The act of laying down palms and cloaks also comes from royal parades. When Jehu was anointed as king, "They hurried and took their cloaks and spread them under him on the bare steps," (2Ki 9:13).
All of this fanfare, though, often hides the grim ending of Holy Week. On Thursday, we will celebrate the Passover, Last Supper, and betrayal of Christ. We reenact the Passover and Lord's Supper ever time we partake in communion. We reenact the betrayal far more often, every time we reject the grace of God and sin against him. On Friday, we will remember the Lamb and his sacrifice in order that death may not come to us. Those who celebrate the coming of the King today will call for the death of a radical teacher on Friday. Even the palms with which we celebrate will be burned and on Ash Wednesday of next year, we will receive them as black crosses on our foreheads to remind us of our mortal nature and dependence on God for existence.
It is not until Sunday, Easter, in one week, when we will find the glory of the empty tomb and see the Son of Man and the Son of God as the Firstborn From Among the Dead. It took God one week to create the world and so in one week, we experience the glory of his final teachings, and death. He rests on the seventh day and on the beginning of the next week, we witness his resurrection. The Temple is about to be destroyed, but we do not fear because it will be rebuilt after three days.
Edit: Mitch Lewis, far more qualified to speak on the subject and much better at expressing his points, has this to say about Palm Sunday.