Tim O'Brien is writing the truth about how he killed someone during the war, so later on his daughter can read it when she's an adult.
O'Brien killed the Vietnamese man walking down the trail. He threw a grenade at him, Tim didn't want to kill him but he did it before he realized it.
Tim O'Brien thinking about what he did to that man because it still bothers him sometimes. He says when he closes his eyes he can still see the man walking and smiling, then trying to run from the grenade and cover his, but didn't succeed.