This statement is made to Amir as he is recovering from his injuries after his encounter with Assef. His scar is on his upper lip and looks like Hassan's scar from his childhood surgery. It is ironic on two counts.
First, Amir's scar on the outside finally represents the scars on his heart from what he had endured and done years ago. He was scarred by his father's treatment of him and by his cowardly action toward Hassan. Now, the scar he wears on the outside shows his redemption. He finally stood up to Assef on behalf of Hassan (by rescuing Sohrab).
Secondly, the scar is ironic simply because it is so close to Hassan's. Amir has just learned from Rahim Khan that he and Hassan are half brothers; so the scar serves as one more bond between them. It demonstrates that Amir was not so different from Hassan after all.