The Ugly Duckling is the most real story about differences and what it means to be different especially when the choice of being different is not yours. Having something unique about your personality which the others do not have and do not realize is one of the most valuable gifts that someone could ever has.
Telling us his story Hans Christian Andersen wants to say that the truth is hidden deep under the cover and one day it comes out into the open. The fact that you are different should not make you sad but happy because when your talent and beauty come to light then the rest of the world will have nothing else to do but just stand in admiration before you.