Moments of assonance help to give the poem its poignant music. (We've only highlighted a selection of assonant moments here; there's much more to find!)
For instance, listen to the vowel sounds in the poem's final lines:
Thanks to its tenderness, its joys, and fears,
To me the meanest flower that blows can give
Thoughts that do often lie too deep for tears.
The plaintive long /ee/ sound that threads through these final lines evokes the speaker's emotion and insight as he communes with a flower. That /ee/ links "me," the speaker, to that "mean[]" (or lowly) flower—and also to his "fears," his "tears," and his "deep[est]" insights.
The sounds thus reflect what's going on here: the speaker is feeling an intense connection with even this most ordinary little bit of nature, seeing himself in it—and thus coming into contact with a profound truth about life. Through this flower, he can feel that nature, the "human heart," and eternity are all mysteriously linked.
A tiny spark of assonance does similar work earlier on in the poem, too:
Not in entire forgetfulness,
And not in utter nakedness,
But trailing clouds of glory do we come
From God, who is our home:
There are just a couple of echoing vowels here: the /ay/ of "nakedness" and "trailing," and the /uh/ of "come" and "from." But those subtle repetitions helps to create the effect that the speaker is launching into the heavens in these lines. First, he leaps from the humility of "utter nakedness" to the splendor of "trailing clouds of glory"; then, he suggests the ease and simplicity with which souls "come / From God."