Shall we start with the lazy answer? You got it: "The Things They Carried" is the title of the first short story in the book, and therefore O'Brien chose it as the title of that book. Done.
As we're sure you're aware, it would be unwise to leave it there. So here it goes: "The Things They Carried" (the short story version) is an account, in lists, of everything the soldiers carried as they marched through Vietnam. The things they carried are in some cases physical (weapons, equipment, personal items) and in some cases intangible. It's the intangible things that O'Brien really focuses on in the book as a whole, whether it's emotions such as love or guilt, each other's guilty consciences, the weight of America's expectations, or the land of Vietnam itself. So the initial short story introduces the idea of soldiers carrying things both physical and intangible, and O'Brien carries that idea forward throughout the remainder of the book. So the title quite properly labels the book: it's a whole piece about all the things soldiers carried.