What does Palm Sunday mean to me? That sounds like the beginning of a bad essay I wrote in CCD a long time ago.
So really, what does it mean? The reading of the Passion reminds us that Jesus entered Jerusalem in triumph, but within days was crucified. I have always thought of it as a statement of human fickleness. Within the period of five days, the people went from hailing Jesus as the Messiah to screaming for his death.
But I think it is something more. During the reading of the Passion, the congregation steps in for the mob. We are the ones calling for Jesus to die. Rather, I am. It is my sins, my failings, my transgressions for which Jesus died. Yet I am still offered the redemption that the cross bought us.