This is a wider-than-usual stole used to give blessings at Weddings, Baptisms and other sacramentals outside of the Mass instead of the usual stole and chasuble. This vestment is worn directly above choir dress, as opposed to the regular stole which is vested over at least the alb.
It is also donned to impart a blessing on pilgrims of faith received in audience by a prelate or when a priest or bishop will bless a home, agricultural field or village on his journeys. For this reason, sometimes it is referred to as a Blessing Stole.
The Pope uses his to receive Catholic heads of State, and also to impart his Urbi et Orbi Blessings from the Balcony on Easter and Christmas Day. All priests - from the local curate to the Bishop of Rome himself, make use of these.
This particular Pastoral Stole in Liturgical White we've made for a Bishop - hence the green lining, proper to that dignity. His arms and other devices embroidered will be featured at a later post - after he receives it later this month from a grateful member of his congregation.
Who knows? Maybe the recipient is you! If you're a bishop. Otherwise, you could always have one made by contacting us - perhaps as a gift to your local priest or friend in the episcopate.