According to Kipling, the "burden" of the White Man is people in less-developed countries.

According to the second line, Kipling believes the burden must fall upon the best.

In the third line, "exile" refers to

Exile refers to the "mission" from which America's young white men might not come back from. The mission being bringing "civilization" and stopping famine and disease in the Philippines

Explanation:

"Go bind your sons to exile"

Not knowing what to expect but still go for the sake of bringing "civilization".

Answer: the colonization and civilization of, white men a country can offer, colonies abroad

Explanation: just did the question