This is a tatted lace butterfly trim. If you don’t know what tatting is, it’s a lost art of tying knots with crochet thread, embroidery thread, or sewing thread.
There are a wide variety of patterns that can be tatted. This trim can be sewn around the collar, the waistline, or the bottom of a dress. Tatting can also be sewn as an edging around a pillowcase or tablecloth. Scrapbookers use lace trim to embellish their pages.