Kipling primarily looks upon colonial subjects as backward and primitive, as considerably less developed than the white man. The picture he paints of colonial subject peoples ("half devil and half child") is deeply offensive in its suggestion that there's something strangely exotic and dangerous about them. As such, he asserts that their savage, lawless impulses must be kept in check by the firm, controlling hand of the white man, whom Kipling regards as their racial superior.
At the same time, Kipling is keen to stress just how onerous the burden of the imperial project really is. He wants to give his American audience the benefit of British experience in managing an empire—to show just how difficult the imperialist project can be and why it's so important to adopt the right attitude. Establishing an empire will be a long, hard process, but it will be worth it in the end, he argues, not least because Kipling regards it as vital that the benefits of Western civilization are conferred upon the so-called lesser races.
The attitudes toward African and particularly Asian (Kipling wrote "The White Man's Burden" about American deliberations over invading the Philippines) peoples expressed in this poem are complex. Kipling clearly sees colonial peoples as inferior to whites. He describes them, after all, as "half-devil and half-child." He does not think they can possibly be sophisticated enough to appreciate the benefits of civilization, and those who try to bring it to them will earn "the blame of those ye better." Kipling is also completely convinced that imperialism, because it brings the alleged benefits of Western civilization to "inferior" peoples around the world, is a noble pursuit. These racist attitudes are as typical of Kipling's time as they are repugnant today. But Kipling's condescension aside, he is urging the wealthy, privileged, comfortable classes in the Western world to put aside self interest and serve others. The fact that the people who were the alleged beneficiaries of this "service" might not see it as such does not occur to Kipling, however. He sees colonial peoples as helpless and primitive.