Hosanna: Hosanna comes from a Hebrew expression that means “save, please” or “please save us.” By the first century AD, Hosanna was not used as a literal cry for rescue from enemies. Instead, it had become an expression of joy and celebration (like the phrase used today, "Praise the Lord!"). For the people, it was an enthusiastic welcome for a famous traveler, "the prophet from Nazareth in Galilee" (Luke 19:38–40; Matthew 21:11).
The miracle of raising Lazarus from the dead might have contributed to the excitement of the day (John 12:9–11). But even the disciples did not fully understand this event until later (John 12:16).
For Jesus, this event was a fulfillment of prophecy. Jesus prepared for the occasion carefully and offered himself to the people of Israel as the Messiah (the Christ, God's chosen king).