Shooting an Elephant

"He wears a mask and his face grows to fit it." What do you think Orwell means by this?

Orwell uses this metaphor to describe transformation. He means that he has forced himself to act a certain way, to be a certain person that is not who he thought he was. Eventually if we act a certain way we run the risk of actually becoming that person and that is what he is saying. If you wear a mask, if you act like someone you're not, then you will grow to fit, you will become that person whether you like it or not it's almost out of your control if you aren't careful.

Note: a metaphor is a figure of speech in which a comparison is made where one thing is used to designate another making an implicit comparison.

Since your question asks for a personal opinion, I'll give you my opinion of what this statement means. You have to interpret it in its context:

Here was I, the white man with his gun, standing in front of the unarmed native crowd--seemingly the leading actor of the piece; but in reality I was only an absurd puppet pushed to and fro by the will of those yellow faces behind. I perceived in this moment that when the white man turns tyrant it is his own freedom that he destroys. He becomes a sort of hollow, posing dummy, the conventionalized
figure of a sahib. For it is the condition of his rule that he shall spend his life in trying to impress the "natives," and so in every crisis he has got to do what the "natives" expect of him. He wears a mask, and his face grows to fit it.

The narrator represents Imperial Britain, and as such the people expect him to behave as their caretaker. At the beginning of the story, the narrator says that many people hate him, "the only time in my life that I have been important enough for this to happen to me." They hate him for the tyranny that he represents, but they turn to him for help in a crisis. That is what Orwell means when he says that "when the white man turns tyrant it is his own freedom that he destroys."

The mask represents something he is appearing to be but is not.  Over time, however, the mask becomes who he is since he has taken on this persona for so long...it eventually actually DOES become part of who he is in reality.