Alliteration fills the poem with music and elevates its language, helping to communicate the speaker's profound feelings of wonder, gratitude, and joy.
The sounds the speaker emphasizes reflect his experience of the world. For instance, listen to the /s/ and /w/ alliteration in the passage where the speaker watches a swimmer:
The swimmer naked in the swimming-bath, seen as he swims through the transparent green-shine, or lies with his face up and rolls silently to and fro in the heave of the water,
The repeated sounds here evoke the gentle swish of water moving around the swimmer's limbs. But these quiet sounds also give this passage a hushed, reverent feeling: it's as if the speaker is so awed by the swimmer's beauty that he has to hold his breath.
Not too long after, the speaker reflects on all the beautiful human bodies he's been observing, and drops in an alliterative /l/:
Such-like I love—I loosen myself, pass freely, am at the mother’s breast with the little child,
Here, the long, liquid /l/ sound again evokes what the speaker is feeling and experiencing: it's a luxurious, languorous sound, and it evokes the pleasure the speaker takes in the people around him. (Note that consonance adds to the effect, with those internal /l/ sounds in "myself," "freely," and "child.")
But this moment of alliteration also tells readers something about the speaker's philosophy. The /l/ connects his "love" to his "loosen[ing]," for instance—suggesting that, for the speaker, part of love is a feeling that he can let go of his own separate personality and inhabit other people's experiences, not just admiring but becoming that "little child."
(Note that we've mapped alliteration only in the first two sections of the poem here—there's plenty more to find!)