The cope is a semicircle of cloth, and its ancestry is the pluviale, a hooded rain cape. The hood is still there, reduced to a flat ornamental shield hanging at the back that no longer functions as anything, and the front is held closed by a clasp called the morse, which in wealthy foundations was a goldsmith's object in its own right, set with stones and sometimes with relics.
Because the cope is a semicircle of unbroken cloth it offers the largest continuous surface of any vestment, and it therefore attracted the most ambitious embroidery. That matters particularly for England. Between roughly 1250 and 1350 English workshops produced embroidery of a quality that was exported across Europe and known on the continent as opus anglicanum, work of the English, using silk and gold thread in a technique of underside couching that allowed the metal to lie flexibly. Popes and cardinals commissioned it, and inventories of the papal treasury list more of it than of any other national work. The Syon Cope and a small number of others survive, mostly in museums, and they are among the finest textiles of the European Middle Ages.
The cope also survived the Reformation in England where most vestments did not. It was retained in cathedral use under the Elizabethan settlement, being arguably a processional garment rather than a Mass vestment, and that technicality preserved a continuity of English liturgical textile that would otherwise have broken.
Its use today is broad precisely because it is not restricted to the celebrant of the Eucharist. Cantors wear it, lay ministers wear it in some traditions, and it appears at processions, Benediction, solemn Evensong, weddings and funerals without a Mass.