The first part of the answer is the easiest: O'Brien's title, in part, refers to all the items carried by the soldiers in the stories. For example, they all carry items necessary to do their jobs, such as their rifles, knives, can openers, water purification tablets (and Kool-Aid to kill the taste of the purification tablets). As individual soldiers are introduced into the stories, we see that some carry bibles (Kiowa, for example), and Ted Lavender even carries tranquilizers to help him deal with fear. The medic, Rat Kiley, along with all of his medical equipment, carries M&Ms to give to soldiers who are fatally wounded and may find some hope in the "medication"--in Vietnam, many medics really did carry M&Ms for those situations.
The second set of things they carried is much more complicated. Many of the soldiers carry talismans to keep them safe: Lt. Cross carries a pebble he received from Martha, which he sometimes puts in his mouth; the machine gunner wears his girlfriend's stocking around his neck. Carrying such talismans is a typical way a soldier tries to enhance his survival and control his fear--he's hoping that the pebble or the stocking will somehow protect him.
Among other things they carried, O'Brien tells they "shared the weight of memory. . . . Often, they carried each other, the wounded or weak," that is, as a unit they've become like one person, and as a single entity, they carry all the memories of what each individual soldier has done or has suffered. When one soldier is wounded or killed, they are all diminshed, and they carry this knowledge with them always. They even carry the fear of being afraid and not doing their jobs, which is arguably the most pervasive fear among combat troops.
The things they carried, according to O'Brien, were not only physical things like weapons, talismans, medical gear, and water but also, and more important, such things as fear, love of each other, love of life, and a drive to keep in other alive.