The Barbette – a strip of fabric, a band around the cheeks and chin. Women wore barbette in the 13th and 14th centuries. The band was usually white, but sometimes with decorative trim, such as a gold border. The barbette was often worn with a fillet, crown, or veil. Sometimes all at once. In the 15th century, veils from other headdresses were tied up in a similar way.
Do not confuse Barbette with slightly similar ones: the Wimple and the Gorget. We had separate posts about them.