Jeffers' use of alliteration favors the sounds of t, d, b, s, k, l, w, m, bl, p, st. A small example is this line, with alliterative consonants in slashes after: "Yet stones have stood for a thousand years, and pained thoughts found" /t/ /st/ /th/ /s/ /d/ /h/. Alliteration is the repetition of sounds. The same sounds can be produced by differing letters or letter combinations. For example, the /s/ sibilant can be produced by a /c/ or an /s/, as in "slice." Similarly, /k/ can be produced by /k/ /ck/ or /c/, as in "keep cycling back." Other sounds he uses are h, f, r, b, th.
Alliteration is most often created with consonants (vowel alliterations are called assonance). Consonants have intrinsic characteristics that create specific effects in prose and poetry. For example, /t/ and /d/ are dental plosives giving off the hardest sounds in English, creating an effect of explosive emotions or events. To further the example, /m/ and /n/ are nasal sonorants giving off among the softest sounds, creating an effect of soothing emotions or events. While Jeffers uses w, m, l, th, r, soothing sounds creating soothing effects, the sounds of t, d, b, f, s, k, bl, p, r, st dominate, creating urgent, cut off, pounding effects. These accord with his metaphors of stone-cutters, time, and chiseling at monuments. The pounding urgency changes with the alliteration here: "and pained thoughts found / The honey of peace in old poems."
An interesting technique Jeffers uses is to tie lines together by repeating the same alliterative sounds in consecutive lines: alliteration is both within lines and between lines. This technique ties lines together, reinforcing meaning. For example, the first six lines are complexly united by alliteration of /l/, /s/, /r/, /th/ between and within lines:
[between] [l,s,r,th] "The square-limbed Roman letters" /l/ /s/ /r/ [within]
"Scale in the thaws, wear in the rain. The poet as well" /s/ /w/ /l/ /r/ /th/ [within] [not s=z in "thaws"]
The meaning Jeffers' alliteration is intended to draw us to is the fight against time, against deterioration, against decay, against oblivion; the fight his poem gives sound to. Looking further into meaning, he draws us to the idea that stone monuments stand "for a thousand years," which he compares to the work of poetry (with softer alliterative sounds), saying old poems give the "honey of peace."
Some effects his alliteration gives are those of the chisel chink and hammer slam of the stone-cutters' work, and the relentless tick-tock of measured time. A critical argument might be made that Jeffers uses an over-abundance of alliteration, that it distracts from comprehending his meaning, and that it subverts his intent through a superfluence of pointed sounds.
To me, Jeffers is trying to tell us that both stone cutters and poets are trying to create things that will last forever. He seems unsure as to whether it's worth it. He says that everything's going to die in the end, but that poetry and stone work can last a long time even so.
I think he uses alliteration to point out the first of these -- that everything falls apart. If you look at a couple of the places where he uses alliteration, they are in the parts where he's talking about this -- both for rock cutters (rock, records, Roman) and poets (blotted, blithe, brave, blind, blackening). I think the alliteration draws our attention to this idea.