Amir seems to encounter quite a few changes throughout the novel, both as a child and as an adult - I suppose narrowing these down to the most significant lessons would be up to you.
As a child, Amir wins the kite flying tournament, witnesses the Russian invasion of Afghanistan, and is forced to flee his homeland, to name a few; however, it seems the most important event is when he witnesses Assef assaulting Hassan: to me, it seems that Amir now realizes he is a true coward, and this is a crucial turning point in Hassan and Amir's relationship.
As an adult, Amir moves to America, loses his father, gets married, has to return to Afghanistan, and many other important events. Perhaps another significant event would be the inner courage he finds when he has to "fight" Assef in order to save Sohrab: I find this section fascinating since Amir seems to take some sort of pleasure in his beating, as if he knows he somehow deserves it. I think this is sort of an awakening for Amir - he now knows he can stand up for himself.
By the end of the novel, Amir is confident enough to stand up to others, such as when Soraya's father attempts to insult his new adopted "Hazara" son - this seems relevant because now we see how Amir has enough self-confidence to stand up for what he believes is right.