How does the narrator meet people's expectations in "Shooting an Elephant"?

The narrator fulfilled the expectations of the natives by shooting the elephant. Because it had caused so much damage and, most importantly, killed a man, the crowd demanded that it be killed even though it had quickly calmed down and appeared to be no further threat. The narrator clearly does not want to kill the animal, but he is determined to avoid, as he says, "looking a fool" in front of the crowd. The fact that the narrator, who is a British colonial police officer in Burma (as was Orwell himself for a time) feels the need to meet the natives' expectations, even when doing so is contrary to his own wishes, is one of the central ironies of the story.

In this story, Orwell is suggesting that imperialism corrupts everyone associated with it, and indeed that the colonialists are, in a way, not any more truly "free" than the colonized. They must act within the perverse, sometimes violent logic of a fundamentally immoral system. The narrator claims, at the moment he was forced to shoot the elephant, he "perceived...that when the white man turns tyrant it is his own freedom that he destroys."

How do the protagonists in "Shooting an Elephant" meet society's expectations?

The main way in which the characters in this essay meet society's expectations is through the shooting of the elephant. Although Orwell himself clearly states that he does not want to shoot the elephant, who clearly was not a rogue elephant and is a creature who is described with considerable sympathy, he reflects that he really has no choice, as the crowds that watch him as a colonial officer and representative of Britain urge him to do so. Note how he explains his reasons for not being able to assert his own independence:

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. He becomes a sort of hollow, posing dummy, the conventionalized figure of a sahib.

This is clearly a very profound meditation on the nature of colonial power, and power in general. Orwell realises at this particular moment that he has no choice but to fulfill society's expectations of his behaviour, even though he has no desire to shoot the elephant himself, because he is only an "absurd puppet" controlled by the will of the indigenous population. Orwell realises that "when the white man turns tyrant it is his own freedom he destroys." The expectation of the crowds and the way in which they controlled Orwell shows the way in which the illusion of colonial power is only that: an illusion, as through seizing power over the Burmese, Britain has only managed to destroy its own freedom. Society's expectations are met in this essay therefore through the killing of the elephant. 

The protagonist of the Essay "Shooting an Elephant" by George Orwell meets the expectations of the society that he finds himself in by shooting the "rampaging" elephant in retribution for it's trampling of a village man. Though it goes against his better judgement, the narrator shoots the elephant and leaves it to die. This satisfies the villagers, and his collegues support him by saying that he did the right thing.