This verse reveals some of the hypocrisy of the title of the hymn. Kipling calls colonialism the white man's burden, but history shows us that colonialism in practice was less of a burden than an opportunity for the colonizer to enrich itself; colonization was more often inspired by greed and gluttony and the constant search for more.
Kipling's poem suggests that through colonization, the "white man" can bring peace to the savage natives, end their hunger, and make them prosperous. As the white man gets closer and closer to the end goal of "peace," the natives can expect an end to their way of life.
At the end of the verse, Kipling warns about the dangers of success if the white man is able to take on this burden. By colonizing the heathen land and civilizing the natives, the white man can expect the natives to become lazy and to continue barbaric religious traditions. The power and control that the colonists worked so hard to achieve and the effort they will spend to "civilize" the natives and make the land prosperous may "all be for naught" (or all for nothing).
Today, knowing all that we do about how imperialism usually played out, we may read this and think that it is satire. Unfortunately, no such luck; Kipling was serious.