If the foreman had no experience in bossing a mob, they had no experience in being one.
-- Narrator (Chapter 1 paragraph 14)

Importance: This quote shows that the people of Anarres do not know how to protest, even when they want to.

Speech is sharing-a cooperative art. You're not sharing, merely eogizing.
-- Unnamed Teacher (Chapter 2 paragraph 33)

Importance: As a child, this is how Shevek is chastised while trying to share a physics joke he finds funny, but no one else understands. This introduces the ideas on Anarres against individualism, an idea that Shevek will come up against again and again in the novel.

This room was evidently for his sole use, as it opened off the bedroom, and contained only one of each kind of fixture, though each was of a sensuous luxury that far surpassed mere eroticism and partook, in Shevek's view, of a kind of ultimate apotheosis of the excremental.
-- Shevek (Chapter 3 paragraph 2)

Importance: This is Shevek's reaction to seeing the bathroom...