"On Shakespeare. 1630" uses alliteration to bring its images and ideas to life on the page.
Take, for example, the rhetorical question posed to Shakespeare in line 6:
What need'st thou such weak witness of thy name?
Those whispy /w/ sounds make the line seem to slip and stumble, as though it's built on wobbly foundations. The alliteration helps to highlight the relative impermanence of objects like statues and monuments, which won't last as Shakespeare's works.
Line 12 then demonstrates the power of the Bard's words to create their own everlasting monument within the minds of readers and theatergoers:
Thy easy numbers flow, and that each heart
Hath from the leaves of thy unvalued book
Those Delphic lines with deep impression took,
The thudding /d/ sounds impress themselves upon the line just as Shakespeare's writing imprints itself on people's hearts. The /d/ has a forcefulness that speaks to the power of Shakespeare's genius.
The speaker expands on this idea, explaining how Shakespeare makes people themselves into a monument for his work:
Then thou, our fancy of itself bereaving,
Dost make us marble with too much conceiving;
The alliteration draws attention to the poem as a made object, something that uses the raw materials of sound and language to create art. More simply, the alliteration just makes the poem itself sound more poetic and emphatic!
In line 15, the speaker describes Shakespeare as "so sepùchlred in such pomp." Those sibilant /s/ sounds (which join up with the /s/ of "dost") add a hush to the line, as though the speaker is telling readers to be quiet out of respect for the sleeping Shakespeare.