Final answer:
The transformation brought on by Hester throwing down her scarlet letter is symbolic of her casting off societal shame and reclaiming her identity, thereby restoring her beauty and strength.
Step-by-step explanation:
The "magic touch" that effects the transformation when Hester throws down her scarlet letter is not so much a physical touch but a symbolic act of casting off the burden of shame and societal judgment that the letter represents. By discarding the scarlet letter, Hester reclaims her identity and the beauty that comes with self-empowerment and freedom from stigma.
Nathaniel Hawthorne uses this transfiguration to symbolize Hester's inner strength and resilience, as well as her ultimate defiance of the community's efforts to define her solely by her past transgressions.