One of the major themes in The Things They Carried is the absurdity and futility of war. As with so many works of literature focusing on the Vietnam War, this novel emphasizes the toll that this futility took on the soldiers. The title--"The Things They Carried"--refers to the psychological weight the war had on these soldiers, which is further symbolized by the gear and the belongings that the soldiers carry with them. Each soldier is characterized by what they carry: Rat Kiley's comic books are an attempt to hold onto youth and American culture, Ted Lavender's small pharmacy speaks to the trauma inflicted on soldiers, and Lieutenant Cross's pictures of Martha are a way of holding onto the real world outside the war, with all its sentimentality and pleasure. When he burns the photographs, he's not only ridding himself of any connections to that outside world but also emphasizing the absurdity of the war itself. He thinks burning the pictures was foolish and a little silly, which by association makes his actions as a soldier foolish and silly, since they're part of a war that's damaging for everyone involved and impossible to win.
Given that a very large part of the story in O'Brien's Things They Carried is about the characters, the theme is reflected in their development and their actions. If you consider the story about the young vietnamese soldier that O'Brien may or may not have killed, you follow the character through the narration and in doing so question the reality and the theme of death on the battlefield and killing on the battlefield.
The way that the incident tortures the narrator and raises so many questions about who the young man was and what his life was like or going to be like before being snuffed out helps to advance the theme and question the ideas that O'Brien is putting forward.