The second part (“A Game of Chess”) of The Waste Land is a sequence of episodes in different styles, all concerned with seduction. (The title alludes to Thomas Middleton’s play A Game at Chess in which the game of chess is used as an extended metaphor for seduction.)
The extract in the question belongs to the second of these episodes, which begins:
“My nerves are bad tonight. Yes, bad. Stay with me.
“Speak to me. Why do you never speak. Speak.
“What are you thinking of? What thinking? What?
“I never know what you are thinking. Think.”
I think we are in rats’ alley
Where the dead men lost their bones.
“What is that noise?”
The wind under the door.
This episode is in the form of a conversation between two people, whom I will call ‘A’ and ‘B’. A’s dialogue is in quotation marks, while B’s is unmarked, and it seems that some of the latter consists of private thoughts rather than spoken words, for A repeatedly interrogates B without seeming to get a response: “Why do you never speak … What are you thinking of?” (This kind of interrogation is also suggestive of a row between lovers.)
Speaker A complains of “nerves”, meaning “disordered or heightened sensitivity; anxiety, fearfulness, tension, nervousness” (OED) and implores B to “stay with me”. Initially we might think that the “nerves” are merely a pretext for A to seduce B, but then A seems really to be fearful about the noise of “the wind under the door”. Perhaps A and B are engaged in an adulterous liaison, and A is alarmed by the least noise, in case it is their spouse returning unexpectedly.
The “rat’s alley” and “pearls” lines are B’s unspoken thoughts about death. The charnel-house rats re-appear in part III of The Waste Land:
White bodies naked on the low damp ground
And bones cast in a little low dry garret,
Rattled by the rat’s foot only, year to year.
while the “pearls” allude to Ariel’s song from The Tempest in which he tells Ferdinand that his father is dead.
Why should B be thinking about death instead of sex? Well, this is the theme of the poem: in the aftermath of the Great War, society is the ‘Waste Land’ of the title, a land rendered sterile like the realm of the legendary Fisher King, in which death, dust, dry bones, and meaninglessness intrude everywhere, even between lovers. (Eliot may also be employing the Freudian idea of the “death drive”, the idea that a psychological drive towards death and destruction complements the drive towards sex and procreation. We know that Eliot was familiar with Freudian theory from his critical works, for example his essay on Hamlet discusses the interpretation of the play in terms of Freud’s ‘Oedipus complex’.)
Throughout the dialogue, the lines have two interpretations, a literal one with respect to the A–B conversation, and a metaphorical one with respect to the theme of the poem. For example, in the conversation, the “wind under the door” is the literal wind, the noise of which A worries might be their returning spouse, and which B tries to soothe away with the reply “Nothing again nothing”. But looking at Eliot’s own notes to the poem (this site has an excellent presentation of them), we find that “the wind under the door” is an allusion to John Webster’s play The Devil’s Law Case, in which two surgeons wonder whether Contarino, who has been stabbed, is dead or alive:
First Sur. Did he not groan?
Second Sur. Is the wind in that door still?
John Webster (1623). The Devil’s Law Case, Act III Scene II.
Here “the wind” is Contarino’s breath and “that door” is his mouth, so in the thematic interpretation, the “wind under the door” is the breath of life, which has become “Nothing again nothing” in the ‘Waste Land’.
Similarly, the lines “Do / You know nothing? Do you see nothing? Do you remember / Nothing?” are, in the literal interpretation, a sordid row resulting from the failure of the speaker’s attempts at seeking intimacy in the thoughts of their lover; but in the thematic interpretation they are a set of rhetorical questions implying that modern people (like the reader of the poem) are “hollow men”, that is, spiritually empty and ignorant.