In his poem, “The White Man’s Burden,” Rudyard Kipling never actually defines the white man’s burden. He says what will happen when people (he was addressing this to the United States) “take up the white man’s burden” and he tells the audience what the white men will feel, but the actual nature of the white man’s burden is only implied.
The white man’s burden was the burden of having to try to “civilize” non-white people. The British had long held colonies populated by non-whites in places like India and Southeast Asia. In 1899, when the poem was written, the US was fighting Spain and would take Puerto Rico and the Philippines (and Guam) at the end of that war. This was to be the US’s first real move towards imperialism and towards ruling over non-white people in other countries.
Kipling says that it is the white man’s burden to have to work hard to try to improve the non-white people. Those people will hate the white colonizers. They will ruin everything the colonizers work for because of their “sloth and heathen Folly.” The white man’s burden is to work hard to help people (“To seek another's profit,/And work another's gain) who do not want to be helped.
The white man’s burden, then, is the set of problems that comes with imperialism. It is the problems that a country faces when it tries to colonize other people and to “civilize” them. In this poem, Kipling is warning that the burden will be heavy and the task will be thankless, but that it will make the United States greater in “The judgment of your (the US’s) peers.”