This question is referencing a passage late in T.S. Eliot's "The Love Song of J. Alfred Prufrock." To put it in context, I've listed the passage in full:
I shall wear flannel trousers, and walk upon the beach.
I have heard the mermaids singing, each to each.
I do not think that they will sing to me (123-5).
To understand this passage, which is one of the most important parts of the poem, you also have to understand the underlying themes of the piece. Like much of Eliot's most famous work, "Prufrock" depicts the emptiness and hollow isolation of modern life. The narrator appears to be a middle-aged man struggling to find meaning and purpose in the crushing context of the modern world. Moreover, if one reads between the lines, it seems the speaker is particularly lonely and longs for a romantic relationship (or at least female companionship). He lacks the courage or assertiveness to actively connect to another person, however, so he seems doomed to a life of isolation.
In many ways, the mermaids' refusal to sing to Prufrock encompasses this theme of isolation. Cut off from romance and meaningful human relationships, Prufrock encapsulates his loneliness by imagining singing mermaids, seductive beings and potential allusions to the sirens in The Odyssey. Based on the context of the poem, we can assume the mermaids do not sing for Prufrock because he lacks the confidence or ability to develop meaningful human relationships. Moreover, by asserting that the mermaids do not sing for him, Prufrock displays his belief that he is a completely uninteresting, hopeless, and undesirable individual. It's a sad image, and one that neatly encapsulates Eliot's gloomy vision of modern life.