I am assuming from the question that you want to come up with a thesis for Orwell's essay. You can do so by isolating one theme, such as the narrator's conflict between being true to himself and doing his job as colonial policeman in Burma. Burma at this time was a British colony and the Burmese people lived under the thumb of the English who had to constantly demonstrate they were in charge. One thesis statement might be: In a world where appearances are more important than reality, people and animals suffer.
An elephant has gone on a temporary rampage and killed a Burmese man. As the local policeman, the narrator, who is an Englishman, is expected to kill the elephant. He goes to do so with the villagers following behind him. By this time, the elephant has calmed down and is not threatening anyone. The narrator really does not want to kill the animal. It is pointless. But he knows the villagers expect it and will consider him cowardly and weak if he walks away. To keep up appearances, to show the Burmese that the British are courageous and in control, he shoots the beast. It is not easy to kill an elephant, so the animal dies slowly and painfully. The narrator feels terrible about what he has done to keep up appearances. ""I often wondered," he says at the end, "whether any of the others grasped that I had done it solely to avoid looking a fool."
Orwell leaves the reader wondering what the narrator should have done. In a better world, the narrator could have followed his own heart and spared the elephant. But Orwell makes the point that in a world where the British must at all costs keep up appearances, individuals end up violating their consciences. Nobody wins. Ultimately, he is saying that we need to build social systems that give people the freedom to act humanely.