In my opinion, what this taught Orwell is that the people who are supposedly in control in an imperial system (the colonizers) are not truly in control. They are often forced to do things that they do not think are a good idea or even things that they do not think are morally right. They have to do these things simply to maintain their image and their ability to seem to be in control.
Orwell feared that the natives would think he was weak if he did not shoot the elephant. If they thought he was weak, he and all English would look bad. This would make it harder for them to control their native subjects.
So the point is that when you start to imperialize, you are no longer able to act based on your own convictions and values. Instead, you have to act so as to keep your control over your subjects.
That those who are in control are often controlled is clearly a point to George Orwell's "On Shooting an Elephant." Because of the British rule and control over the Burmese, the Burmese themselves placed certain expectations upon their rulers. Here is the irony of power, an irony that Orwell feels intensely as he feels it contingent upon himself to destroy the magnificent animal. It is equally ironic that the animal Orwell must shoot as he does the "dirty work of Empire" is an elephant, so often symbolic of power.
And as the poor beast dies slowly and in great agony with the "mysterious, terrible change" coming over him, the elephant also becomes symbolic of the of slow death of Britain's great empire.