Collect for Palm Sunday:

Almighty ever-living God, who as an example of humility for the human race to follow caused our savior to take flesh and submit to the Cross, graciously grant that we may heed his lesson of patient suffering and so merit a share in his resurrection. Who lives and reigns with you in the unity of the Holy Spirit, one God, forever and ever.

From the Directory on Popular Piety and the Liturgy, 139:

Palms and olive branches are kept in the home [not for superstitious reasons, but] as a witness to faith in Jesus Christ, the messianic king, and in his Paschal Victory.