“The White Man’s Burden” is a poem written by Rudyard Kipling, which was first published in 1899. Kipling wrote it in response to the Philippine-American War, which started in February 1899.
This poem is widely considered to be very imperialistic, as it mainly deals with the theme that white men consider themselves to be superior to the indigenous people they encounter in the colonies.
The third stanza links strongly to this theme. To Kipling, the white man’s burden is the fact that white colonialists are destined to help the indigenous people of the colonies to develop and improve their lives. He sees this improvement happening by the colonizers' bringing “peace”, putting an end to “famine” and by “bid[ding] the sickness cease.” However, this is proving to be very difficult, which is what the lines you are quoting refer to.
According to Kipling’s poem, the indigenous people are described as “sloth[ful]” and full of “heathen folly,” which undermines any attempts of the colonialists to try and help them. Interestingly, Kipling uses personification here in order to make his point, as he refers to “sloth” and “folly” as if they were people: “watch sloth and heathen folly bring all your hopes to nought.” It is the folly and the sloth of the indigenous people that destroy all attempts by the white men to bring a better life to the people of the colonies. This difficulty is one of the reasons why Kipling called his poem “The White Man’s Burden.”