I have put this question in the "Shooting an Elephant" group because the original wording of the question made clear that it referred to this story.
One of the major points in this story is that an imperial government must maintain its "hegemony" over the people it rules. Another way to say this is that the imperial power has to keep up its image in the eyes of the people -- it has to keep them convinced that its power is inevitable and that it is in complete control. If it does this, they will be much less likely to want to rebel. This is how an imperial government sustains its political power.
In the story, Orwell has to act with this goal in mind. He has to act in the ways that the Burmese expect him to behave. If he does that, he maintains the image of British power. If he does not (in this case) shoot the elephant, he weakens this image. He must act to maintain the image, no matter what his personal conscience tells him to do.
What an imperial government must do to sustain its power is to control the thinking of the repressed people. It must do this by acting in ways that keep them convinced of its power.