The pallium is the rare vestment that says something about jurisdiction rather than about order. A metropolitan wears it only within his own province and only at certain liturgies, and canon law requires him to request it of the pope within three months of his appointment and forbids him to exercise certain metropolitan functions until he has it. What it signifies, in the standard Latin reading, is a share in the pastoral office of the bishop of Rome, not the archbishop's own dignity, which is why it must be asked for and why the pope alone gives it.
Its beginnings are less clear than its present rules. The band appears in the late antique west without an explanation attached, and its ancestry has been traced to imperial or civil insignia by some writers and to an ecclesiastical honour by others; the sources do not settle the question. Early popes granted it to individual bishops as a personal privilege, and only from the ninth century onward does it settle into the metropolitan requirement it now is.
Compared with the East the difference is instructive. The omophorion, its Byzantine counterpart, is worn by every bishop as a mark of the episcopal order itself and is not granted by anybody. The two garments began close together and have ended saying different things: one about being a bishop, the other about a relationship with Rome.