This poem by Rudyard Kipling makes uncomfortable reading today, but it reflects beliefs that were sincerely held by some at the time. Kipling certainly does, as you say, suggest that imperialist nations are helping those they colonize. We can see this where, for example, Kipling describes imperialists as having gone "to serve [their] captives' need" or "work another's gain."
Kipling gives some pragmatic examples of how he believes imperialists to be helping the imperialized—imperialists "bid the sickness cease" and "fill full the mouth of famine." In practical terms, there is an element of aid in that the colonizers might be physically improving the lot of those in the countries they have invaded. Despite the fact that the so-called "savage" people do not want them there, there is a suggestion that they need their colonizers all the same.
In spiritual terms, there is also some help being offered, Kipling suggests, to the invaded peoples. It is the duty of the colonizers to lead the people they meet towards "the light." These are not Christian people, and so it is by spreading the word of the Western God with them that the imperialists are able to help these people in spiritual terms, by saving their souls and introducing them to Christianity.
Obviously these views are very problematic to the modern reader. Kipling is suggesting in this poem that it is by eradicating the existing cultures of these countries that the imperialist powers have best "helped" them. However, Christianity remained a potent force behind imperialism at this time. Many people did genuinely believe that it was their duty to take Christianity to those who had not been introduced to it and that this was the best way to help them.