What does "the real motives for which despotic government acts" mean?
I think that you are just asking for an explanation of the quote. So I will give you a shorter answer that just explains what that quote means.
First of all, the word "despotic" refers to a government that rules without really caring about the people it rules. Such a government does not care what those people want. This type of government only cares about what the rulers want. So a "despotic" government is sort of like a dictatorship or a tyranny.
The word "motives" refers to the goals that cause the government to ask.
So the phrase you have provided really means "why do despotic governments act the way they do?" The first answer tells you why they act as they do (in Orwell's opinion).
Despotic governments result from the need to maintain power over subtly resistant people. The real motives reveal that such a government can rule only by fulfilling the people’s expectations and responding to every crisis with the expected force. Orwell points to the irony that he stood armed in front of an unarmed crowd, yet he was powerless to do as he wished or as his judgment told him. Instead, he felt himself “an absurd puppet pushed to and fro by the will of those yellow faces behind” (7).
The first two paragraphs introduce us to the alien, far-off world where the narrative took place. In addition to setting the scene, Orwell explains what he was doing in Burma and, more importantly, gives us an emotional perspective from which to view the event. We learn in a general way about the bitterness between the colonialists and the native inhabitants and about the psychological effect his job as a policeman had on him. His confession that he was “young and ill-educated” and not even aware the British Empire was collapsing helps us feel empathy for him in the incident that follows. Without this information, we might not be willing to forgive him the shooting of the elephant or its horrible death, or comprehend the sense of victimization he felt despite his position as an “authority.”
Orwell uses analogies in important places. Two of the analogies are from the theater and relate to the sense of falseness that Orwell feels about his role in the colony. With the crowd watching him, he compares himself to “a conjurer about to perform a trick” with “the magic rifle.” Then he helps us to understand his own psychological state at that moment by using another theater image: “Here was I . . . seemingly the lead actor of the piece; but in reality I was only an absurd puppet pushed to and fro by the will of those yellow faces . . .”; in the East, he says, the white man “becomes a sort of hollow, posing dummy. . . . He wears a mask, and his face grows to fit it” (7).
Paragraph 10 continues this analogy, as Orwell describes the crowd breathing “a deep, low, happy sigh, as of people who see the theatre curtain go up at last.”