"The White Man's Burden" by Rudyard Kipling is a quite complex poem. While superficial readings have tended to associate the phrase "The White Man's Burden" with imperialism, colonialism, and paternalistic racism, the poem itself, and Kipling's work in general, displays considerably more in the way of nuance.
The most common sense of the phrase refers to the obligation of the Englishman to take up the burden of colonial administration as a duty. This sense of duty was based on two notions, one of noblesse oblige, the sense that people in a position of power have a duty to help those less fortunate, and a religious sense in which many Christians of the period felt a duty to bring their religion to non-Christian nations. In British history and culture, this meant that the motives for colonialism were mixed, combining economic incentives and geopolitical power with a sense of moral obligation.
In the poem, Kipling does invoke the image of colonial service as a sort of test of manliness, but the tone is rather heavily ironic. In the poem, Kipling alludes to the liminal position of the British colonial culture, in neither being respected at home in Britain nor appreciated by the natives who resent the British as conquerors, as is apparent in the following lines:
Take up the White Man's burden,
And reap his old reward--
The blame of those ye better
The hate of those ye guard--