Alliteration adds intensity and emphasis to the poem, making the Earth's plea for freedom sound all the more compelling.
The first stanza is packed with /d/ alliteration: "darkness dread & drear," "dread" (again), and "despair." These thudding sounds are like hammers pounding throughout the poem, conveying the immense weight holding the Earth down. Broader consonance, highlighted below, adds to the effect:
Earth rais'd up her head,
From the darkness dread & drear.
Her light fled,
Stony dread!
And her locks cover'd with grey despair.
These /d/ sounds have a dull, punishing insistence. The many guttural /r/ sounds in these lines (as in "dread & drear") add a low growl to the lines as well.
Alliteration adds yet more rhetorical power to the Earth's speech in the second-to-last stanza. In line 17, for example, the bold /b/ alliteration of "buds and blossoms" help to capture the sudden, vibrant beauty of spring. In the next lines, the alliteration of "Sower"/"sow" and "plowman/"plow" elevates the poem's language—and, thus, add power to the Earth's argument. Note that these are also examples of the device known as polyptoton, which links both characters (the "Sower" and the "plowman") with the action they perform (sowing and plowing). This emphasizes that such work (and the sexuality, freedom, creativity, etc. it represents) is entirely natural.
In the final stanza, the alliteration of booming /b/ sounds intensify the Earth's call to be freed:
Break this heavy chain,
That does freeze my bones around
Selfish! vain!
Eternal bane!
That free Love with bondage bound.