Throughout the course of this poem, Prufrock reveals, through the stream-of-consciousness style of writing, all of his insecurities and fears about himself and his life. He cares greatly for a woman, and wants to express his feelings and ask her something (experts suppose a marriage proposal), but he is worried that she will reject him and mock him. He is worried that she does not feel the same way at all, and that he will make a fool of himself by revealing his feelings when they won't be returned. So, in his imaginings, he imagines himself growing old; part of the imagry involved with growing old is reflected in the phrases "his hair is growing thin," and "but how his arms and legs are thin," and other such things that happen to men when they grow old. They look and dress a certain way. The reference to him rolling his trousers is another allusion to old men; right before that reference, he declares, "I grow old! I grow old!" So, we know that is on his mind. Old men tend to wear their trousers rolled up a bit to avoid tripping. So, he is worried that he is too old and insignificant, and that she will view him as a crazy old man, and that he will grow old alone.
The mermaid reference is a connection to women; mermaids are mythical, beautiful creatures, women, who, in fable, tend to lure men to the depths of the sea with their beauty, and then the men drown. So, Prufrock referring to the mermaids simply shows his attitude towards women: they are alluring, beautiful, untouchable, unattainable creatures that leave him in pain, drowning in insecurities. They only sing to people they desire, and he feels that he is undesirable, which is why they won't ever sing to him.
I hope that helped; good luck!