Two long strips of material, most often lace, that hang from the top of the head down the back or over the shoulders. They can be extensions of a cap band or any sort of headdress. Lappets were a required element of female court dress from the early 18th through the early 20th centuries.
The print shows a detail from "Costume de Présentation" from the French magazine Journal des Dames et des Modes, July 31, 1814. After the restoration of the Bourbon family to the monarchy in 1814, French court dresses seen in prints show many of the same elements of English court dress, including lappets.