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."