Hosanna, in Greek, is an exclamation of adoration or praise (Strong's Concordance #G5614). It is recorded only five times in six KJV New Testament verses (Matthew 21:9, 15, Mark 11:9 - 10, John 12:13).
"Hosanna" branches were often carried by those marching in processions during their celebration of the Feast of Tabernacles in Jerusalem. These branches were commonly from palm, myrtle or willow trees. This tradition became so popular that the seventh day of the Feast was aptly known as the Hosanna Day (1906 Jewish Encyclopedia).
Hosanna derives its origin and meaning from the Hebrew phrase translated as "save now" as is found in Psalm 118.
Save now (yasha na, #H3467 and #H4494), I beseech thee, O Lord: O Lord, I beseech thee, send now prosperity (Psalm 118:25, KJV).
New Testament usage
All six occurrences of this word revolve around either Jesus' triumphal entry into Jerusalem or the events involving him the next day. His triumphal entrance took place on Thursday, March 30 in 30 A.D. He began his journey from Lazarus' house in Bethany, and then went to Bethphage and from there to Jerusalem. As he approached the city, cries of "Hosanna!" were heard in the crowd.
. . . a great crowd of people who had come for the feast, when they heard that Jesus was coming into Jerusalem, took branches from palm trees and went out to meet Him, and were shouting, "Hosanna! Blessed is He Who comes in the name of the Lord, the King of Israel" (John 12:12 - 13, HBFV).
The parallel accounts recorded in Matthew and Mark (Matthew 21:9, Mark 11:9 - 10) also record that "Hosanna!" was shouted by those who witnessed the Lord coming in the city. John's account of the incident, however, adds an important detail.
The Apostle John states the people were also proclaiming Jesus was the prophesied messianic King of Israel. Luke's account mentions the Pharisees becoming so incensed at such pronouncements that they demanded the Lord rebuke such praise. Jesus, of course, refuses to do as they wish (Luke 19:39 - 40).
The next day
Jesus, on Friday, March 31, visits the temple and throws out the moneychangers as he did at the start of his ministry. After he heals the blind and lame, children at the temple begin shouting "Hosanna!" Once again, the Jewish religious leaders, this time the chief priests and scribes, are furious and warn the Lord about this rejoicing.
But when the chief priests and the scribes saw the wonderful things that He did, and the children shouting in the temple and saying, "Hosanna to the Son of David," they were indignant,
And said to Him, "Do You hear what they are saying?" Then Jesus said to them, "Yes! Have you never read, 'Out of the mouths of little children and infants You have perfected praise'?" (Matthew 21:15 - 16).
Jesus, no doubt restraining himself from giving a much sterner, and deserved, rebuke, again dismisses concerns about the cries of "Hosanna!" meant for him.