"The repetition of stressed, initial sounds" -- specifically, consonant sounds. An awful ass, a beastly boy, crepuscular creature! Die dreadfully!. Alliterative effect is when the sound is unstressed, or isn't at the beginning of the words.
Early English poetry is typically alliterative rather than rhyming: Beowulf, Sir Gawain and the Green Knight (there are several translations out there, including one by Tolkein!), etc. Fred Chappell used a similar technique in his poem "My Grandfather's House Goes Up." You can use alliteration more subtly -- enhancing certain words or phrases, rather than dictating the poem's form. The Handbook suggests scanning your poems for any alliteration to make sure you aren't overdoing it. As always, reading aloud helps you use this tool most effectively!
I don't know which came first -- my love for alliteration or my enthusiam for early english epics -- but i've enjoyed this technique as long as i can remember. The only poem from my preteen years that i haven't utterly destroyed begins,
"Alone, aloof / a lioness
Lay languidly / as her prey passed."
We watched a lot of Nature and Nova on PBS back then.