It appears that the Gospel of John (12:1) puts Jesus’ Triumphal Entry on the Sunday before He is hanging on the Cross – Good Friday. This is the beginning of His Passion Week.
While neither Matthew, Mark or Luke mention palm branches – John does (12:13), and that makes the day Palm Sunday. Earlier in the day Jesus sends two unnamed disciples to the village of Bethany on the eastern side of the Mount of Olives.
They found the donkey just as Jesus told them it would be (prearranged or supernatural?) and brought it to Jesus. Riding a donkey does not sound like an impressive entrance, but it followed Old Testament traditions and fulfilled prophecy (Zech 9:9).
Huge crowds joined Him along the way, many carrying palm branches (probably having nationalistic symbolism). Matthew (21:8-9) notes they spread clothes and branches on the road in front of the donkey and spoke of Jesus in prophetic terms – “Hosanna to the son of David”).
It must have been an amazing few hours of exuberance for the disciples. But Jesus understood the bigger picture – basically the same crowd that celebrated Him on Sunday would be calling for His Crucifixion on Friday morning!
Mark is precise about what happened next (11:11). Upon arrival in Jerusalem, Jesus went onto the Temple compound and observed all that was happening. That evening He left the Temple with His twelve Apostles and headed back to Bethany on the Mount of Olives to spend the night.