At the beginning of Heart of Darkness, Marlow is talking about the Romans. He talks about how the Romans were nothing but thieves and murderers. They were unable to actually rule other peoples. After speculating on how the Romans felt, he says
Mind, none of us would feel exactly like this. What saves us is efficiency—the devotion to efficiency.
Efficiency, then, is what Marlow thinks separates British imperialism (and perhaps other imperialism) from the imperialism of ancient Rome. Ironically, the rest of the book shows that this idea of modern efficiency is totally illusory.
In the context of imperialism, efficiency simply means exploiting the colonized country without wasting resources. It means that the imperial power will go into a backwards country and use modern methods to make sure that the goods (like the ivory that Kurtz is getting) that make imperialism worthwhile will come out in a constant flow. It means that the imperial power will act rationally. It will not allow its resources (like the sunken steamer at Central Station or the laborers at Lower Station) to be wasted. The reason that Europeans deserve to be imperial powers (in this view) is because they do not waste resources like natives do.
Efficiency in imperialism, then, has to do with extracting the most possible resources with the least possible amount of waste. It is not something that the white imperialists in Heart of Darkness achieve.