Alliteration is quite a prominent feature of "Because I Could Not Stop for Death."
Technically speaking, alliteration is first used in the /h/ sounds of line 5—"He knew no haste"—but it's the next example that seems more significant. In line 7, the speaker relates how she "put away" her "labor" and "leisure," in part because Death was so "kindly" and civil towards her. In other words, she felt duty-bound to leave aside both her work and her play.
These, perhaps, are the two key factors in most people's lives: the work that people do (labor) and what they do outside of that work (leisure). Both are, of course, incredibly open-ended. Labor doesn't need to mean paid work—it could relate to domestic work at home, or even writing poetry. And leisure could be anything from hobbies to spending time with loved ones. Accordingly, the alliteration that joins these two words emphasizes the way that they are such key parts of what it means to be human. It makes them more prominent, suggesting their deep-rooted importance.
In the following stanza (stanza 3), the poem intensifies its use of alliteration. Here, each line has a pair of alliterating sounds:
We passed the School, where Children strove
At Recess – in the Ring –
We passed the Fields of Gazing Grain –
We passed the Setting Sun –
This alliteration emphasizes the way that each location the carriage passes represents a different stage of life, whether literally with regards to childhood or metaphorically in the figure of the setting sun (representing the end of life). The alliteration draws attention to each line, making them feel like distinct units, almost like signposts coming into view.
Another example of alliteration is in lines 15 and 16. Again, the alliteration comes in pairs:
For only Gossamer, my Gown –
My Tippet – only Tulle –
The alliteration helps make the lines sound delicate, which in turn suggests the thin clothing that the female speaker is wearing.
As one final example, look at line 23. Here, the twin /h/ sounds of "Horses' Heads" recall the sound of horses exhaling as the speaker undertakes her final journey. This use of alliteration, and the poem's use of alliteration in general, helps draw attention to the specificity of its descriptions.