Palm Sunday is the start of Holy Week - the last week before Jesus' death and resurrection. There was a lot of celebrating on Palm Sunday. The people in Jerusalem were waving palm branches, putting those branches and their coats on the ground to make a path for Jesus. They were cheering and saying:

Hosanna to the Son of David! Blessed is he who comes in the name of the Lord! Hosanna in the highest! -Matthew 21:9

Throughout the rest of the week, Jesus spent time in the temple and saw people selling things and making money instead of praying and worshiping God. He also had a meal known as the Last Supper with his disciples, where he served his friends by washing their feet. He prayed In the Garden of Gethsemane, but was then arrested and put on trial. 

Jesus knew that all of this would take place, and he knew what was going to happen next...that he would die on the cross and shed his blood to wash away the sins of all people.