Matthew 21:9

That went before] These were the multitudes mentioned by St. John, who went out from Jerusalem to meet Jesus. Those who followed behind were the Galileans. Hosanna to the son of David] This can only mean, Glory and honour to the Son of David,' just as St. Mark's phrase, 'Hosanna in the highest,' is translated by St. Luke, 'Glory in the highest (heaven).' How 'Hosanna' comes to have this meaning, is disputed. It is taken from Psalms 118:25, where it is addressed to God, and means 'Save (us) now.' Probably it had become a mere exclamation of praise, 'a kind of holy hurrah,' the consciousness of its grammatical meaning being lost, as in the case of 'Alleluia.' This is clearly the case in the 'Didache,' which has the phrase, 'Hosanna to the God of David '(Did. 10).

The exclamation 'Hosanna' was used chiefly at the Feast of Tabernacles. The seventh day of that feast was called 'Hosanna Day,' and the branches carried by the worshippers were called 'Hosannas.' The events of Palm Sunday are thus an imitation of the ritual of that festival.
It is sometimes said that the well-known classical custom of carrying palms in token of victory was unknown to the Jews of our Lord's time; but certainly the palms carried Revelation 7:9 seem to be symbols of victory.