The repeated M sounds in the first line of the poem ("I caught this morning morning's minion…") make a kind of humming noise that gets us thinking of the hum of the wind under the windhover's wings. Then, the repeated D in the next line sounds like the abrupt, staccato beat of the bird's wings as he skillfully repositions himself on the wind, like a surfer.
Almost every line has alliteration of some kind ("rung upon the rein;" "wimpling wing"), and the end rhymes all sound similar, too—they all end in -ing. The sameness of the sounds imitates the bird's motionlessness in the air, as he hovers and harnesses the wind. The alliteration and rhymes sound like the whooshing of the wind under the bird's wings.
You hardly have to move your mouth at all as you read the poem—you can murmur it quietly, while admiring the absolute control of the bird over the air and the poet over the words.