There's a good deal of alliteration in "The Poplar Field," a poem that uses a rich range of sonic effects to communicate and emphasize its ideas. In a general sense, alliterative groupings like "fell'd, farewell," "cool colonnade," "favourite field," and "long lie as lowly" just make the poem more memorable, musical, and emotionally impactful for the reader.
It's useful, though, to examine some specific moments of alliteration in detail. In line 1, the repeated /f/ sound between "fell'd" and "farewell" heightens the tragedy of the line and links the trees' destruction to the speaker's mournful goodbye. Combined with the strong mid-line pause, or caesura, the assonance on the vowel sound /eh/ ("fell'd" and "farewell"), and the consonance on the /l/ sound ("fell'd" and "farewell"), this first instance of alliteration strongly connects the two halves of the line. The stark revelation that "[t]he Poplars are fell'd" carries into the speaker's moving "farewell" to the beloved grove of trees.
The alliteration of "cool colonnade" in line 2 displays a very different use of this sonic device. Whereas the repeated /f/ sound of line 1 communicated a sense of tragic dignity, the second line's repeated /c/ sound is joyful, gentle, and wistful. The alliteration reflects the relaxation and pleasure the "cool colonnade" used to bring the speaker. Similarly, the alliteration on the /f/ sound in line 6 emphasizes, in a straightforward but moving way, the genuine affection the speaker has for this "favourite field."
Line 14 shows another way in which alliteration contributes to the overall effect of the poem. The speaker's realization that "I must e'er long lie as lowly as they" picks up on the /l/ sound that has been repeated in subtle ways throughout the poem since the first line ("The Poplars are fell'd, farewell to the shade"). Now, though, the speaker looks to the future, not the past or present, and the close alliteration makes the moment stirringly emotional. Though the speaker is by no means distraught about the inevitability of death, it's clear that thinking about human mortality has stimulated the speaker's emotions in a profound way. Much of the line's emotional depth—indeed, much of the emotional impact of the poem as a whole—is thanks to alliteration.