Newington in Oxfordshire. The glass dates from the early sixteenth century and was jointly the gift of Dr Stephen Barworth (died 1511) and Dr Richard Salter (died 1518), they were both fellows of All Souls College, Oxford and sucessively rectors of Newington. The image portrays one of them (we don't know which one) dressed in choir dress. He is wearing a pileus or doctor's bonnet on his head and you can see he has a very full surplice with long sleeves. Over the surplice he wears a fur garment which forms a cape over the shoulders, has a hood attached and two pendants that hang down at the front. This fur garment is the Almuce. The Almuce was a vestment of dignity worn by cathedral dignitaries and it seems also by those who had acquired a master's or doctoral degree from one of the universities. The type of fur used varied according to the rank of the wearer, grey squirrels' fur being reserved for canons and bishops. The almuce was still worn in some places during the Elizabethan period, but it gradually fell out of use to be replaced by the black silk tippet. In the Roman Catholic church it evolved, in most places in the mozetta or shoulder cape.
Here is another example, worn here by Master Thomas Butler (died 1494), who was rector of Great Haseley, Oxfordshire:
More on the history and form of the Almuce here: P. Dearmer, The Ornaments of the Ministers (London, 1908), pp. 133-136.