A Shadow is the suppressed self, thoughts or emotions that the original doesn't want anyone to know or even acknowledge themselves. When released the Shadow becomes the embodiment of those unwanted thoughts or emotions. I believe that Twilight's Shadow would be a pompous queen obsessed with how special she is and believes she can never fail, as the original Twilight seems to hate the idea of taking the slightest bit of pride in herself and her utter fear in failure that always present. This is just my perception as a Persona fan boy, it's not like these things will ever be covered in the show.