The theme of universal brotherhood is one which rejects all racial, social, religious, economic or other forms of classification or heirarchy, and instead makes the argument that all men are of one blood. It should be noted that, in the time that Eliot was writing, it was common to refer specifically to men, rather than men and women or all mankind, because Eliot is discussing shared experiences and lives that, in that era, were experienced only by men.
Universal brotherhood suggests that, at pivotal moments in one's life, or during great actions, our more superficial differences fade, and in their place we see only our common elements; our humanity, our emotions, hopes and sufferings. We experience greater empathy for other humans and wish for their success and happiness just as we wish for our own.
Eliot's poem does not spend the majority of its length discussing death, dying or war; rather, it begins by talking about common feelings that humans share;
A man’s destination is his own village,
His own fire, and his wife’s cooking;
To sit in front of his own door at sunset
And see his grandson, and his neighbour’s grandson
Playing in the dust together.
This introduction establishes the centrality of brotherhood as a theme in this poem; all men desire a home, family, comfort, and the simple pleasures that come with them. A soldier from India desires this just as much as a soldier from England. Dying in Africa, as these soldiers did, left them just as far from their homes as it would any English soldier.
The poem is seeking to evoke a sense of sympathy for these dead soldiers; they were not just Indians, but men, whose loss will be felt by their families just as deeply as an Englishman's, and who probably felt, in their final moments, very distant from the things and people that they loved, and very much alone.