The "white man's burden" is a phrase popularized by Rudyard Kipling in his 1899 poem by the same name. This concept was not meant to help impoverished areas of the world.
The phrase refers to the idea that the white people who came to colonial nations—nations administered by more powerful countries—did so out of a sacrificial sense of duty to help the native peoples living there. The underlying assumption behind the phrase was that white people were superior to darker-skinned peoples and that European culture and religion were more advanced than native cultures and religions. The presence of white people, Christianity, and western culture was therefore a gift bestowed on native peoples that could only benefit and elevate them from a "savage" to a civilized state.
This is an example of a mystifiying ideology. A mystification is a story or theory that fogs or mists up reality to try to obscure people from seeing what is really occurring. The belief that white people colonized non-white countries primarily for the benefit of the natives kept people back at home from understanding that these colonial and imperial ventures were, in fact, primarily for the economic benefit of the ruling nation. The ruling nations needed the resources these other countries could offer them, and rather than using these resources to help the so-called backward countries, the European powers exploited native peoples by robbing them of their resources at very low prices. Second, as Europe was faced with over-production—it produced more goods than it could sell—the colonized countries became captive markets for these surplus goods.
European and other governments knew that they had to make colonialism sound palatable to their own populations, but the reality was that these powerful nations pillaged the lands they ran for their own benefit. The "white man's burden" concept was a reversal of reality: native peoples bore the burden of the white presence. We know this because of the many well-documented instances of extreme poverty, exploitation, and atrocity in colonial territories across the globe.