Water symbolism runs throughout The Things They Carried. Water usually symbolizes baptism and renewal, but in O'Brien's novel it infects and kills. But, years later, the Song Tra Bong, the river whose banks overflow and drowns Kiowa, is a place which triggers O'Brien's memories and inspires his stories.
Mary Anne survives swimming in the Song Tra Bong, whereas the innocent soldier, Kiowa, is swallowed by it. Morty Phillips swallows a mouthful of it and dies, and Bowker, the professional soldier, kills himself because of its stench. The Song Tra Bong is both a rite of passage and a sirens' song, and once baptized by it, one longs to return to it (to bury Kiowa's moccasins) and be tortured by it (Bowker's suicide). And lest we not forget that O'Brien could have been saved from the whole Vietnam experience by a swim across a different river.
The shitfield where Kiowa died is a metaphor for the Vietnam War itself. The land war in Asia is often referred to in similar terms as a "quagmire," which is literally a swamp, bog, marsh, or mire. Figuratively, a "quagmire" is a mix-up, mess, predicament, quandary, confusion, sticky situation, or dilemma. Personally, I like "shitfield" better than them all. The Vietnam War stinks and kills, literally and figuratively.
So, the field symbolizes Vietnam, the quagmire of the Vietnam War, the death of Kiowa, the death of Tim's innocence, and the place where so many of Tim's memories are buried that he must return to it, with his daughter, so she too can tap into its source for storytelling.