Kite fighting, and kite running more specifically, represents sacrifice, loyalty and friendship. Hassan had always been loyal to Amir and always ran for him, early in the novel declaring "for you a thousand times over!" The act of kite running for them was like a ritual establishing and sustaining their bond of friendship. When Amir stood by while Hassan was raped and framed Hassan with stealing the money, it becomes clear that Amir is not loyal to Hassan. Hassan even accepts the blame as a last loyal sacrifice to Amir. Their friendship is severed here and with Hassan leaving, their kite fighting ends as well.
Dealing with guilt in the subsequent years, Amir tries to make amends by rescuing Hassan's son, Sorhab. The novel ends with Amir running for Sorhab as Hassan ran for Amir. Amir returns the sentiment Hassan had given him, telling Sorhab, "for you a thousand times over!" This reestablishes a bond within Hassan, through his son, and gives Amir the opportunity to become as loyal to Sorhab as Hassan had been to Amir.