This delicate fabric is known as pierced work from the technique with which it is decorated.
Accessories made using the technique became fashionable during the late eighteenth century. Fine fabric, either linen or silk, was stiffened by starch so the threads would stick together. Then the fabric was punched using fine rounded metal teeth to push the threads aside rather than severing them, creating a lace-like pattern.
Examples of pierced work can be seen in waistcoats of the 1780s and 1790s, such as: 835-1907, in the V&A collection.
Larger examples of pierced work such as this veil: T.314-1920, and apron: T.313-1920 are included in the V&A Textile and Fashion collection.