Hosanna, or hosiah-na, was an acclamation of the Jews: when applied to God, means save us, I beseech Thee; when applied to a sovereign prince, means vivat, in Latin, or long live the king. (Bible de Vence)
Hosanna, says St. Jerome, is the same as, Save, I beseech thee. (Psalm cxvii.) Some will have the word Hosanna directed to Christ himself, and the sense to be, Save us, O thou Son of David; others understand Hosanna, directed to God, as if the people said, Save, O Lord, this our king; by which the people wished peace, safety, and prosperity to Jesus their Messias. (Witham)
It appears that the Holy Spirit, on this occasion secretly inspired their tongues, and through their means caused loud thanks to be offered to Jesus, for an approaching blessing, of which as yet they had no conception.
These same words of acclamation are daily used in the preface of the mass, and represent the exultations of both priest and people, expecting, as it were, and rejoicing at his coming. (Bristow) ...