Alliteration adds musicality and lyricism to the poem. Though the speaker uses lots of dense, scientific language, alliteration (plus frequent consonance and assonance) means that it still sounds pleasing and poetic.
For example, listen to the alliteration in lines 6-7:
blind bones with their manipulating tendons,
the knee and the knucklebones, the resilient
The alliteration adds emphasis to these body parts, and it also generally heightens the poem's language. In this way, alliteration helps to convey just how incredible the human body is.
Alliteration also emphasizes the intricate connections within the body. For example, notice how the phrase "miniature to minute" evokes the way the cartilage of the ear curves inward, like the concentric revolutions of a seashell, getting smaller and smaller closer to the ear canal. The same sounds slip across the line as the words themselves shrink (moving from "miniature" to positively "minute").
Alliteration also overlaps with consonance and assonance. Together, these devices make the poem sound richly musical and memorable, and they also evoke the images being described. Just listen to the crisp /t/ and /k/ sounds in the phrase "intricate exacting particulars"; the sharp, quick consonance itself feels intricate, exacting, and particular.
Another passage dense with sound patterning comes at the start of stanza 2. There's the alliteration of phrases like "sharp cresent [...] shell-like complexity," as well as broader consonance of /k/, /s/, /sh/, /t/, and /n/ sounds:
Observe the distinct eyelashes and sharp crescent
fingernails, the shell-like complexity
of the ear, with its firm involutions
concentric in miniature to minute
ossicles. [...]
This latticework of sounds evokes the interconnected nature of the body itself, which functions because it has countless links between all these seemingly disparate parts.
The second half of the stanza is likewise filled with alliteration, consonance, and assonance. /C/, /m/, /l/, /n/, and short /i/ and /n/ sounds trickle down the page, lending a kind of connective musicality to the long lists of complex words. Take lines 14-16:
ossicles. Imagine the
infinitesimal capillaries, the flawless connections
of the lungs, the invisible neural filaments
Again, the richly layered sounds suggest just how beautifully complex the body itself is.
Finally, notice all the plosive /p/ alliteration in the poem's closing stanza: "passion," "possessed," "practice, "perfectly," "precision." These sounds evoke the speaker's biting tone: they seem to be almost sneering at "passion" and "sentiment," which compared to biology are clumsy and inaccurate and impossible to understand.