Semana Santa

Yesterday began Semana Santa, which I think is the week between Palm Sunday and Easter Sunday. It's relatively embarassing for a Religious Studies major to have to ask this question, but... why "palm" Sunday? Everyone in the whole city was walking around and hanging out at churches all day with big woven palm fronds in the shapes of crosses and other origami-like designs... I could Google it, but I figure I'll offer this one up to my virtual studio audience: what's the connection between palm trees and Jesus?