Till human voices wake us, and we drown.
Eliot is setting us up with this fantastical, romantic ideal of mermaids and beautiful ocean views. Once you wake up to the knowledge that the ideals of romance are a fantasy, you die a little inside.
Eliot is also alluding to Homer’s Odyssey; the “sea-girls” are the Sirens, whose song is so beautiful that no man can resist it. It causes the sailors to throw themselves into the sea and drown or crash their vessel into the rocks and die.
Prufrock is living in a superficial, pretentious society in which he is constantly being judged for his looks, actions, etc. This is the only external identity he knows, but “waking” to it from his own inner life, he essentially “drowns"—his life is empty and meaningless.
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