The protagonist of T. S. Eliot's "The Love Song of J. Alfred Prufrock" is a middle-aged man, socially awkward and somewhat shy, who is attracted to younger, beautiful women. He is very conventional and afraid of violating social rules.
The mermaids in the poem represent the unattainable women to whom he is attracted. The fact that they are mermaids, fantastic creatures who inhabit the ocean, emphasizes that they are objects of fantasy rather than realistic aspirations.
I agree with the other educators that the obvious reference is to the Sirens, beautiful and fatal women in Homer's Odyssey who lure men to death with their songs.
The stanzas also strike me as echoing Matthew Arnold's "The Forsaken Merman," a poem that would have been known to Eliot. Although the genders are different, much of the imagery is similar. In particular, Eliot's description of the undersea world evokes the Arnoldian one:
Sand-strewn caverns, cool and deep,
Where the winds are all asleep;
Where the spent lights quiver...
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