While there's no clear physical setting to be found in this poem, we can talk more broadly about the historical backdrop to "White Man's Burden." In fact, it's about time we did just that.
As we mentioned over in the "In a Nutshell" section, this poem came out in 1899, right after the end of the Spanish-American War. Now, it doesn't take a detective to figure out that this was a war fought between Spain and America, but it didn't actually take place in either Spain or America. Instead, it was fought in places like Guam, Puerto Rico, Cuba, and the Philippines. That's because these were all Spanish colonies, countries that had been previously taken over and run by Spain—at the expense of all the people who were living there before the Spanish showed up.
When America won the war against Spain, then, it also won control over these colonies. This poem encourages white men to head overseas—and Kipling was specifically thinking about the Philippines when he wrote—in order to spread white, European "civilization."
From our modern perspective, this idea is clearly a bunch of poppycock, but it was actually a widespread sentiment at the time this poem came out. Thanks to hundreds of years of landing on foreign shores, enslaving local inhabitants, and taking all the natural resources back to their homeland, Europeans (some anyway) had come to see themselves as a superior "race" of people. There was even a kind of "science" to this idea, which tried to measure things like skin tone, skull size, and facial features in order to determine how "advanced" a human being might be. (Spoiler alert: the whiter you looked, the more advanced you were thought to be.)
So, this was a not a fun time to be a non-European, non-white person. Countries like England, Belgium, Portugal, Spain, and eventually the United States were taking over foreign lands (called colonies) in a bid to expand their empires. And some saw this expansionism not as a political maneuver, but instead as a way to lift up the colonized people to the same standard of living as the colonizers. That's the idea, at least, that motivates the speaker of this poem. (For more on him, check out our "Speaker" section.)
Not that anybody bothered to ask whether the local inhabitants wanted or even needed any "civilizing," of course. They were seen as so undeveloped that they couldn't possibly know what was best for them. Yeah, it was a pretty dark time for anyone who believed that a person was just a person—no matter where she lived or what she looked like. We're glad we've moved past the horrors of colonialism, but its legacy of racism is one that—centuries later—we've unfortunately been unable to get rid of entirely. Bummer.