The 'White Man's Burden" refers to imperialism.
It is the title of a poem written by Rudyard Kipling in 1899, after the Philippines were under the control of the US.
He aimed to highlight the irony behind this situation in which the US, a nation that fought so hard to achieve freedom from its colonizers, had become a worldwide powerful nation and was taking control over other territories as the European colonizers did in their land centuries ago.