How we cite our quotes: Citations follow this format: (Chapter.Paragraph)
Quote #1
And if you are not needed by your brother men, there is no reason for you to burden the earth with your bodies. (1.20)
Equality 7-2521 expresses the basic principle of his society here. It holds that human individuals are a burden and have no reason to live unless they can be of use to others and the greater good in some way. This ultimately makes each individual feel guilty for being alive. The message is that individuals need some higher reason (serving others) to live aside from themselves, or else their existence is unjustified. It is exactly this idea that Ayn Rand militantly rejects as false morality, and Equality 7-2521 himself will realize this by the end of Anthem.
Quote #2
We shall never leave this house," we said, "nor let it be taken from us. This is our home and the end of our journey. This is your house, Golden One, and ours, and it belongs to no other men whatever as far as the earth may stretch. We shall not share it with others, as we share not our joy with them, nor our love, nor our hunger. So be it to the end of our days." (10.15)
Equality 7-2521 has invented the concept of private property here. He's claimed a "home" for himself and his beloved, and doesn't intend to share it with anyone else. It belongs to him as an individual, and to him alone, just like his hunger and the love he feels for certain other individuals. Having a physical space and objects that belong only to oneself is seen as an important dimension of freedom by Rand, who made private property central to her political philosophy. She asserted that private property is crucial for separating oneself from the potentially oppressive presence of other people. As Equality 7-2521 will say later on, human freedom is freedom from other people.
Quote #3
I wished to know the meaning of things. I am the meaning. (11.4)
Equality 7-2521 has discovered the word "I," and with it the central truth of Randian egoism. Before he wanted to know what things in the world "meant," and what the meaning of his own life was. But he's now found out no such meaning exists. His life has the meaning he gives it. And it's not Collective 0-0009 humankind that gives it this meaning – it's him, as a unique individual.