What does this sentence mean: "this was one chance to become someone who was looked at, not seen, listened to, not heard"?
The way this quotation reads is a bit confusing, but if we know the context of the statement and we understand Amir's relationship with his father, it helps us understand what Amir means.
All of his life, Amir has felt that Baba is disatified with him. This leads him to feel that he is "seen," but not really "looked at," and "heard," but not "listened to." Have you ever felt that someone is seeing you but is not really looking at you? Have you ever felt that someone is listening, but does not really hear you? The person about whom you feel this way is not giving you the attention that you believe you should have.
If Amir can win the kite contest, he believes his father will finally really look at him and hear him. Sadly, it takes Amir until almost the end of the story to understand the underlying reason for what he perceives to be his father's lack of attention, but once Amir and Baba reach the United States, Baba does behave in a way that makes Amir realize he is loved. The relationship between Amir and Baba before Baba dies is one of the many redemptions in the novel.