Amir, in his childhood, behaved in ways that caused grievous wrongs to Hassan and Hassan's father. In fact, it could be reasonably said that his behavior played a part in their deaths.
While Amir is generally arrogant and domineering to Hassan when they are children, the first really striking wrong we see in the novel is when Amir hides in an alley while a group of bullies sodomize Hassan.
Since the presence of Hassan in the household is a constant reminder to Amir of his own wrongdoing, he manipulates events so that Hassan is accused of a theft, and that causes Amir's father, Baba, to "exile" Hassan and Hassan's father, Ali, from the household.
Because of the subsequent upheaval in Afghanistan, Amir and Baba are forced to flee the country. Had Hassan and Ali remained in the household, there is a good chance they would have left for America with Amir and Baba. Both must remain and both die.
A chance to be good again is a chance for redemption, which is a prevailing theme of the novel. While Amir and Ali have died, Amir has left a son behind, Sorhab, who will have no chance for a good life unless Amir can rescue him. Such a rescue is a way for Amir to overcome his own cowardice, atone for his sins against the family, to redeem himself in his own eyes, and to save one child from a terrible life or death.
You will notice that the book opens with the idea of redemption and closes with the redemption, telling the reader what a powerful and important idea this is in the story.
Baba did not "exile" them from the household. Baba forgave Hassan for the theft, that he did not commit, and Ali and Hassan chose to leave. Baba was heartbroken that the two decided to leave. The quote means that since Amir decided to do nothing while Hassan was in the alley getting raped and that he framed Hassan for theft, he must come back to Kabul and get Hassan's son from the orphanage and bring him back to a couple that would care for him. The qoute tells us that Amir can reedem himself for what he had done in his childhood