Throughout "Sunday Morning," alliteration helps to add emphasis to certain images and ideas while also making the poem's blank verse more musical and memorable.
In line 5, for example, the breathy, whispery alliteration of "holy hush" evokes the very quiet being described. The smooth /w/ sounds in lines 11-12 work similarly, creating a sensation of smooth, silent movement:
Winding across wide water, without sound.
The day is like wide water, without sound,
This entire stanza is filled with broader sibilance as well (which is often, though not always, alliterative) :
Upon a rug mingle to dissipate
The holy hush of ancient sacrifice.
She dreams a little, and she feels the dark
[...]
Seem things in some procession of the dead,
Winding across wide water, without sound.
The day is like wide water, without sound,
Stilled for the passing of her dreaming feet
Over the seas, to silent Palestine,
Dominion of the blood and sepulchre.
All those /s/ and /sh/ sounds cast a somber hush over the stanza and help to transport readers into the woman's mind. The smooth, hissing sounds subtly evoke the way religious guilt slithers into her consciousness and darkens the bliss of her Sunday morning solace.
At other moments, alliteration (and the related devices consonance and assonance) can help to link different phrases. In the second stanza, for instance, the alliteration in the phrases "balm or beauty" and "pleasures and all pains" connect the ideas being compared. In the first example, it's because they're similar (earth's soothing "balms" are part of eath's "beauty"); in the second example, it's because they're two sides of the same coin (a full life is marked by both "pleasure" and "pain").
Finally, alliteration can simply make the poem sound more poetic or emphatic. Take the lilting /l/ sounds of "littering leaves" in line 75, the forceful /b/ sounds of "burning bosom" in line 89, or the threatening hiss of "savage source" in line 95. For another example, note how the repeated /m/ sounds in "[l]arge-mannered motions to his mythy mind" create a sense of drama and grandeur worthy of a god's thoughts. Similarly, the heaving /d/ alliteration of "Downward to darkness" in line 120 adds drama to the poem's final moments.