Hosanna: a shouted cry of welcome and praise, drawn from an old prayer for rescue, used to hail Jesus as the promised king
Hosanna began life as a prayer. It is a Greek spelling of a short Hebrew cry from Psalm 118:25, "save, please!", a verse every pilgrim knew by heart from the songs sung at the great festivals. Over the centuries that prayer was chanted so often, while crowds waved palm and willow branches around the altar, that it hardened into a set shout. By the time of Jesus it worked less like a sentence asking for something and more like a sacred cheer, in the way "hallelujah" is praise rather than a request.
That is why every place the word appears in the Gospels, the crowd is using it to welcome Jesus into Jerusalem as the long-awaited king in David's line. The way the shout is built shows the shift: people cry "Hosanna to the Son of David" and "Hosanna in the highest," phrases that make no sense if the word still simply meant "save us now." You cannot literally pray "save now" to someone, or "save now" up in the highest heavens. The cry has become an act of honoring a king, slotted into a festive, royal welcome.
The older prayer never fully disappears, though. Anyone in the crowd who knew the psalm would still hear the echo of "save, please," and a number of scholars argue that on this charged day, with a Davidic figure riding into the city, that plea for national rescue was still alive in the shout. So the single best way to read the word is as two things at once, weighted toward praise: a holy shout of welcome that still carries the memory of a cry for help.
Luke leaves the word out of his account of the same scene and writes "glory in the highest" instead, which fits the idea that by then the cry simply meant praise. The earliest Christians kept using it the same way, even directing it to God in worship, and the church has preserved it ever since in the "Hosanna in the highest" of its services.