First, Orwell made the analogy between skinning a rabbit and the effect that the elephant had on the dead Dravidian coolie. By doing this, Orwell shows how dehumanized he felt at the time -- he was unaffected enough by the man's death to compare him to an animal.
Second, he makes the analogy between the elephant and a piece of machinery. This helps us feel like the elephant is useful and ought not to be killed.
Finally, he draws the analogy between himself and a magician that the crowd has gathered to watch. This shows us that he feels that he is on display and that everyone will watch and judge his actions.
1. "As a police officer I was an obvious target and was baited whenever it seemed safe to do so." Analogy: A police officer is a target; a police officer is a symbol of imperialism; the natives bait him; the natives are victims of imperialism.
2. "When a nimble Burman tripped me up on the football field and the referee (another Burman) looked the other way, the crowd yelled with hideous laughter." Analogy: the white soccer player is a tripped by a native; the native referee looks the other way; the native crowd yells and laughs. Orwell the white soccer player is a symbol of imperialism the same way Orwell the police officer is. He is baited and targeted by the natives for public ridicule.
3. "Its mahout, the only person who could manage it when it was in that state, had set out in pursuit, but had taken the wrong direction and was now twelve hours' journey." Analogy: The elephant'ss mahout is a foreign master, much smaller than the captive elephant just as the British are the foreign imperialists of the Burmans, much smaller in number, but able to maintain control.