“The multitude goeth forth to meet our Redeemer with flowers and palms, and payeth the homage due to a triumphant Conqueror: the Gentiles proclaim the Son of God; and their voices thunder through the skies in praise of Christ: Hosanna in the highest!
“A great multitude that was met together at the festival cried out to the Lord: Blessed is He that cometh in the Name of the Lord: Hosanna in the highest!
“Near the descent the whole multitude began with joy to praise God with a loud voice for all the mighty works they had seen, saying: Blessed be the King who cometh in the name of the Lord; peace on earth and glory on high.“
–From the Procession of Palms, Palm Sunday (EF)
Palms are a sacramental, an object that brings your blessings. Don’t buy palms from someone outside the church (this is actually a thing in some places). Go to Mass and receive them. Take them home, and put them in a prominent place, near a statue, or a religious image. Keep them there until your parish asks for them next year. They’ll be used to make the ashes for Ash Wednesday. Don’t throw old palms away!