The term "white man's burden" comes from the infamous poem by Kipling in which imperialism is viewed as an ideal because the white man is supposedly bringing civilization and "higher values" (whatever these were alleged to be) to non-white peoples throughout the world.
Kipling's poem is marked by a defensive tone, in which he seems to suggest that those who "take up [the] burden" will be criticized and unappreciated for having done so. This arguably indicates that there is something wrong with imperialism, even from the standard imperialist perspective. Britain and the other governments did not really need a flag-waver like Kipling to back them up, for they had already long attempted to rationalize the project of taking over other countries under the cover of "civilizing" them. The real object of colonialism, however, was theft—theft of the resources of what would later be called the Third World. The European leaders, or some of them, perhaps did believe they were carrying out their project for selfless reasons, but if so, this attests to the endless ability of people to believe their own PR, no matter how irrational it is. There were admittedly many missionaries who genuinely thought they were saving the souls of Asian and African peoples by converting them to Christianity, though in view of this as a goal, it is astonishing how few people they actually managed to convert over a period of over two hundred years of imperial rule.
In view of some of his other writings, as well as the somewhat strained tone of "The White Man's Burden," one almost wonders if Kipling is being slightly ironic when he phrases the purpose of the British effort as
To seek another's profit,
And work another's gain.
The idea that it was somehow not for its own profit that a despotic government acted, from today's perspective, seems almost surreal. Kipling appears, moreover, to recognize the "futility of the white man's dominion in the East," to use Orwell's phrase (though Kipling blames this on the colonized people themselves, and does so in typically demeaning terms):
And when your goal is nearest,
The end for others sought,
Watch Sloth and Heathen Folly,
Bring all your hope to nought.
Yet, as Orwell pointed out in his essay on Kipling, the stereotyped view of the poet as a vulgar chauvinist is not as true as it appears. In "Recessional," Kipling acknowledges the wrongness of empire and is prescient in seeing that the "white man's burden" thinking has in effect already been discredited:
The tumult and the shouting dies,
The Captains and the Kings depart....
Far called, our navies melt away,
On dune and headland sinks the fire,
Lo, all our pomp of yesterday
Is one with Nineveh and Tyre !
Judge of the Nations, spare us yet,
Lest we forget—lest we forget !
Here, as elsewhere, Kipling's subtext is religion, specifically the idea that "we" have in fact acted wrongly and will be judged by God. This is the furthest thing from the amoral power politics of the period of totalitarianism from 1920 to 1945 which would succeed the heyday of imperialism that Kipling appeared to celebrate.