Symbolism, Imagery, Allegory
This is one special curtsy. Azalea demonstrates it for her younger sisters:
Azalea smiled, inhaled, and touched her right foot in front of her. She traced it in a circle behind her, then slowly sank to the left knee. With strained balanced, she folded herself up as she disappeared into the poof of her skirts. Her legs twisted like pretzels beneath her. She bowed her head, nearly kissing the floor, and extended her right arm above her, her left tucked behind her back. The girls applauded. (9.26)
That's a pretty serious curtsy, right? It takes skill, balance, and lots of practice, it would appear, and it's only supposed to be done "for your husband, or royalty. Like a king" (9.29). Of course, since Azalea's a princess, her husband will be royalty, either by birth, or because of marrying her.
She fears that she may not be able "to give the Soul's Curtsy, with all her heart and soul, to anyone" (9.32), which seems like a legitimate fear, since for all she knows, she might be facing an arranged marriage. In this situation, the Soul's Curtsy represents her ability to truly consent to her marriage—to perform politically and for the good of her family, instead of following her own heart.
Keeper calls it a "graceful, unearthly curtsy" (9.24), and says he wishes he could see it again someday. That day comes all too soon when Keeper, now revealed as the murderous High King D'Eathe, grabs Azalea in order to torture and then kill her: "He twisted her fingers and bent them back, pain coursing to her shoulders, and her knees gave way" (27.17). He makes a mocking reference to the Soul's Curtsy, but luckily the cavalry arrives before he can do anything else to Azalea. And here we see the Soul's Curtsy turning into an ugly parody of affection and consent between two partners—it's a darker take on Azalea's willingness to marry for reasons other than love.
The last time we see the Soul's Curtsy is when Azalea gives it to Mr. Bradford when they get betrothed. This time, "She gave this curtsy her all; every muscle and fiber of her focused on melting into a deep, flawless dip" (30.90). This symbolizes her complete devotion to Mr. Bradford, how much she views him as a worthy partner, and her respect for him—finally the Soul's Curtsy actually symbolizes what it purports to.
And here you thought it was just a little bow…