The Greek word stole means garment. The stole is a long band of silk of the same width and color as the maniple, but three times its length. The priest wears it around the neck and crossed on the breast, and it represents immortality. It is worn by those clergy of the rank of deacon or above when administering the sacraments, as a symbol of the authority of their office. Its color matches that of the other vestments.
A deacon wears the stole over the left shoulder, joined under the right arm; a priest wears it around the neck and crossed at the waist; and a bishop wears it in similar manner, but uncrossed.
—from pages xx and 85 of Treasure and Tradition: The Ultimate Guide to the Latin Mass by Lisa Bergman
This particular stole is worn by the priests of the Fraternity of Saint Peter (FSSP) at Saint Benedict's Parish in Chesapeake, Virginia USA.