Alliteration is a common device in poetry, and it draws attention to itself; the more alliterative a poem gets, the more deliberately crafted it feels. The heavy use of alliteration in "The Lady of Shalott" (so heavy we haven't marked anything close to every instance of it in this guide) thus fits right in with the poem's interest in the nature of art itself. All those repeated sounds never let the reader forget that they're reading a poem, woven artfully from words as the Lady's tapestry is woven artfully from threads.
There's a particularly strong example in the first stanza of Part II, lines 37-45, where the speaker first introduces the Lady to the reader directly. These lines use heavy alliteration on the /w/ sound with words like "weave," "web," and "whisper," linking together the hushed secrecy of the curse with the repetitive hushed sounds of weaving. The poem here also uses hard /k/ sounds to connect the tapestry's "colours" with the Lady's "curse," and with "Camelot" itself. Here, alliteration evokes the rhythmic, repetitive quiet of the Lady's weaving, and at the same time gives the reader the sense that the Lady's artistic gifts and her curse of isolation are tangled up together. The echoing sounds are both evocative and meaningful.
Something similar happens in the beginning of Part III, when Sir Lancelot makes his appearance. Lines 73-108 are riddled with alliterative /b/, /g/, and /r/ sounds: the "gemmy bridle" that "glitter'd" like a "branch" of the "golden Galaxy" is just one example. The description of the knight is seductively gorgeous, but the sounds are punchy, evoking both the knight's effect on the Lady and his eventual effect on her magic mirror. Lancelot's beauty is a full-force KO, and its sounds echo its power.
In other moments alliteration evokes the imagery or content of a line. Take the hard /k/ sounds of line 115-116:
The mirror crack'd from side to side;
"The curse is come upon me," cried
These sounds are loud and harsh, evoking the smashing of the mirror and suddenness of the curse as it hits the doomed Lady. There is also a great deal of sibilant alliteration in the poem, discussed in a separate entry in this guide.