A cornette is a piece of female headwear that was especially popular in Europe in the 15th to 17th century. It is essentially a type of wimple consisting of a large starched piece of white cloth that is folded upwards in such a way as to create the resemblance of horns (French: cornes) on the wearer's head.
Read more about Cornette: Use By The Daughters of Charity, The Cornette in Popular Culture