British imperialism
Throughout the essay Orwell explicitly discusses the nature of British imperialism, specifically the way that he, as a police officer, both represents and internalizes the imperial project. He opens by revealing the brutality of British colonialism in Burma, with images of tortured prisoners, and he discusses his distaste for the empire's impact in Burma. He says that he's on the side of the "Burman," yet he also resents Burmese people for the way they perceive him. Orwell's self-consciousness as the face of British imperialism is central to his internal conflict as he tries to uphold the image of the impenetrable empire while going against his personal inclination, and killing an elephant that he doesn't want to kill.
Fear of humiliation
Orwell says that the bystanders would laugh at him if he were trampled to death by the elephant, and "that would never do" (34). In this way he is compelled to kill the (now peaceful) elephant. In the way that the elephant, in the essay, can represent the Burmese society, Orwell's fear of humiliation can represent the motive of the broader British colonial project. The imperial police officer is willing to sacrifice his sense of what is right, and to fulfill the role of oppressor and tyrant, in order to save face. The fear of humiliation is one of the most important motives in Orwell's essay.
Colonial resentment
One of the central themes threaded through the essay is the latent resentment of the colonized people of Burma for the British occupiers who aim to control their society, yet cannot fully do so. We see this resentment in the open disgust which the monks reveal for Orwell personally, a sentiment that he feels is hypocritical given their office; we see it in the cruel laughter of the Burmese for the British players on the football field; and ultimately Orwell's awareness of his resentment manifests in his explicit rationalizing for his motivation for killing the elephant.
The performance of power
Orwell describes power as being fundamentally performative; it's also illustrated as such through the heavily allegorical aspect of his act of shooting the elephant. Openly, Orwell discusses the ways that he must uphold the performance of power by not appearing to hesitate in shooting the elephant. With the crowd watching, he must appear to be in control of the situation. The performative element of power subsequently plays out as we watch him, in his role as British police officer, demonstrate his confidence in bringing a wild beast, literally, to its knees.
Taming of the colonized subject
Related to the theme of the performance of power is a clear theme of "taming" that plays out in the scenario of a man controlling a wild beast. Orwell's self-imposed task of upholding the impenetrable image of the British empire is part of a larger goal: to control or "tame" Burmese society. If he falters in his performance, he'll make room for the colonized Burmese to see through imperial control and to subsequently cease to respond to that control.
Police power
The experience of the imperial police officer is an experience of representing the empire as a whole. As the face of the British empire, Orwell is personally subject to the Burmese peoples' derisions of the empire. To them, he is the Empire. By seeing Orwell's personal criticisms of that Empire contrasted with his experience asa representative of it, we are able to reflect on the experience of policing, and of representing state power more generally. The personal feelings, beliefs and ideologies of the officer are irrelevant so long as he is in uniform and thus represents a whole other set of beliefs and ideologies.
Natural life
When we see the elephant grazing in the paddy field, we see the naturalness of its existence. The image of the Burmese inhabitation as a labyrinth of thatch huts is similarly an image of natural life. The presence of the "white man" or the British empire contrasts with this naturalness and literally physically disrupts it. In the way that Orwell's shooting of the elephant reflects a form of vandalism of natural life, so to do the beatings of Burmese bodies and the imperial policing of Burmese society.