Alliteration is an important feature in "Strange Fruit." The first instance is in line 1:
Southern trees bear strange fruit,
The two /s/ sounds here link "Southern" with "strange." That is, they tie the "strange[ness]" of the fruit to a specific geographical location—the southern United States. Lynching predominantly took place in these states, and the alliteration gently reinforces this link.
The next example is in line 2, with the strong repetition of /b/ and /l/ sounds:
Blood on the leaves and blood at the root,
Black bodies swinging in the southern breeze,
The two /bl/ sounds chime together, suggesting an abundance of blood (in turn suggesting the horrible violence that caused blood to be on the tree in the first place). "Black bodies" in the following is then linked via sound with this "blood," making it clear this "blood" has been spilled by black people. The loudness of these two voiced /b/ consonants also adds weight to the suddenly explicit way in which the poem clarifies what exactly "strange fruit" means (the terms of the poem's extended metaphor). In the same line, the "swinging" bodies are again specifically linked to "southern" America.
The second stanza features alliteration of the /s/ sound, also known as sibilance:
Pastoral scene of the gallant south,
Scent of magnolias, sweet and fresh,
Then the sudden smell of burning flesh.
This sibilance becomes even stronger when considering the /s/ sounds that pop up in the middle of words too. There's an almost sickeningly sweet sensation to having so many /s/ sounds in such close proximity, and this plays on the grotesque tension between prettiness and ugliness that runs throughout the poem. The magnolias smell "sweet" and beautiful, small proofs of nature's beauty—but the same air that carries their fragrance also carries the sudden and horrific smell of "burning flesh."