Symbolism, Imagery, Allegory
The tignon is a stylish headpiece that wraps around the wearer's head rather than sitting on it like a hat. It figures in one major scene in the book:
Cass's wispy hair was tied up in one of Calinda's tignons. It made me smile to see Cass switching her skirts down the stairs like a scrawny, pale reflection of Calinda, including the tignon, tied in a tidy knot. (6.48)
Tilly smiles, but for some reason, Delphine freaks. She rips the tignon off Cass' head and starts yelling at Calinda, while Cass and Tilly are completely befuddled. Delphine chooses not to explain, though, instead only saying, "She has not earned the tignon, your sister!" (6.52) Huh?
Later, we learn that "tignon" is New Orleans slang for a person of color. Delphine says, "I am nearly as white as you, chère. There are others like me paler than yourself, blue-eyed, yellow-haired. Yet as the saying goes, there is a tignon in the family" (12.44). So, a tignon is both something to be earned and a derogatory term.
Without a bit of historical context, which no one in the book really gives, it's hard to understand the significance of the tignon. In 1786, the Spanish governor of New Orleans passed a law that said women of color—whether free or enslaved—had to wear tignons. This was done in particular to keep free women of color in check, to make it crystal clear that they were still second-class citizens. Women pushed back, though, by wearing beautiful and ornate tignons. Ha. And, in this way, the tignon became a symbol of both oppression and pride. (Source) Which explains Delphine's beef with Cass wearing a tignon.