In ancient times, philosophers and teachers commonly wore a pallium, or cloak, draped over their shoulders. Today, a pallium is mainly known as a religious vestment worn by the Pope.
In the Catholic church, a pallium is worn only by the Pope and a few archbishops. This long, narrow band is white, and it has to be knitted at least in part from lambswool from sheep raised by Trappist monks. This garment, which is adorned with six black crosses, has a lot of religious significance to devout Catholics. The word itself simply means "cloak" in Latin.