The symbolism that opens and closes The Kite Runner represents Amir's change.
At the start of the novel, Amir is walking through Golden Gate Park. He speaks of "unatoned sins". As he walks through the park, he sees kites flying. The symbolism of the kites is an emotional one, recalling his life in Afghanistan. It represents a time in his life where he was silent and uncertain of his identity. Combined with Rahim Khan's insistence that there is "a way for him to be good again," the park at the novel's beginning represents promises that are not fulfilled: "I thought of the life I had lived until the winter of 1975 came along and changed everything. And made me what I am today."
When the novel closes, the park symbolizes the journey having come full circle. Amir has found his path "to be good again." Amir has honored Hassan in a way that he didn't when Hassan was alive. Amir has taken responsibility for Sohrab and devotes his life to him. The park now represents promises that have been fulfilled. The kites symbolize a way to connect with Sohrab. As he chases kites with Sohrab, the park represents a new start for both of them.