Amir's quest for redemption in The Kite Runner becomes the most powerful force in his adult life. Amir feels constant guilt over his treatment of Hassan. Their class differences prevented Amir from accepting Hassan as a true friend, but Amir's more direct behavior was more troubling. He failed to come to Hassan's assistance when he was raped by Assef's gang, and his jealousy over Baba's attention prompted him to plant the evidence that seemed to prove Hassan guilty of theft. These cruel truths bothered Amir somewhat before he and Baba left Kabul, but they became overpowering when Amir reached adulthood in California. Amir compensated by becoming even closer to his father, and this contents him somewhat. But following Baba's death, Amir learns that Hassan is also Baba's son, and this fact merely reopens the old wounds. In Amir's mind, there is only one way to atone for his past mistakes: He must make the dangerous trip back to Afghanistan and recover Hassan's son, Sohrab--Amir's own flesh and blood as well. Only in this way will he ever complete his quest for redemption.
Amir spends most of his adult life trying to get redemption in The Kite Runner. Amir and Hassan were the best of friends when they were younger, but as they got a little older, Amir began to resent Hassan in many ways. Amir was born into a family that was wealthy while Hassan was the "son" of Amir's father's servant. Amir's father, Baba, seems to show much affection and attention on Hassan and Amir is jealous of that. Hassan stays faithful to Amir, even after Amir turns his back on his one time friend. Amir feels great guilt about letting Hassan get raped and not trying to help. Amir knows that he was a coward, but he treats Hassan badly after this.
As Amir grows older he lives with this regret more and more. He and Baba escaped to America, but when Baba dies, Amir finally finds out the truth. Hassan is really his half brother. Baba was Hassan's father. This realization hits Amir hard. He struggles with what he had done and what to do next. When he learns that Hassan has been killed by the Taliban, Amir makes the decision to travel to Afghanistan to rescue Hassan's son, Sohrab. Sohrab has been taken by the Taliban and Amir goes to get him.
By the end of The Kite Runner, we see that Amir does what he has to do to atone for his sins. He has lived with his guilt for many years, and now he is living for redemption. He is finally able to get that redemption in the form of Sohrab.