It is usually important to look at the context...
George Orwell's “Shooting an Elephant” is an essay of extraordinary honesty and depth. To look at this essay critically, a reader must look for the meaning beneath the surface. Sometimes this is a little easier said than done.
It is usually important to look at the context in which a work is written. Orwell is writing about his experience as a British police officer in colonial Burma. Burma at this time was still a part of the British Empire. As such, it had been subjugated to some degree, as all colonial countries are. This subjugation often leads to resentment on the part of the indigenous people, a resentment that sometimes becomes dangerous for the colonial power.
The essay, as the title indicates, involves the shooting of an elephant that has escaped its owner and wreaked havoc in a village. If we are reading critically, we have to ask ourselves why Orwell would bother to write about this experience. In this case, Orwell explains part of his purpose directly:
And it was at this moment, as I stood there with the rifle in my hands, that I first grasped the hollowness, the futility of the white man's dominion in the East. 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.
Orwell is communicating the idea that a colonial power will eventually destroy itself. It doesn't take a lot of critical thinking to get Orwell's point here, he spelled it out for us. But, since this passage appears just past the halfway mark of the essay, Orwell isn't done yet. The rest of the essay shows Orwell tracking and finally killing the elephant. What's important here isn't so much the actual killing of the elephant, but how it happens.
Orwell spends over half a page describing the killing of the elephant. It takes many shots, and the creature does not die neatly or quickly:
His body did not even jerk when the shots hit him, the tortured breathing continued without a pause. He was dying, very slowly and in great agony.
Now is the time to read and think critically. The essay's historical context should tip us off to the symbolism that Orwell is employing. The elephant exemplifies the occupying power, the British. Like the British, he is an undesired presence, causing problems, even death, in the village. The Burmese, in the same way that they want to rid themselves of the elephant, also want the British out of their lives.
Orwell sees a future in which the British will suffer the same fate as the elephant, a long, painful, difficult decline. It ended in death for the elephant; for the British it will end in the withdrawal of their forces.