Admiral Dunfee is a former Navy man, a self-described "Fish out of water" (4.29.49), and in charge of the Graveyard. He brings unwinds there illegally and has them do work in exchange for keeping them safe until they turn eighteen. It's his way or the highway, and he calls his rules—including things like "You are better than those who would unwind you" (5.32.10), and "Make something of yourself" (5.32.20)—his Ten Demandments.
He never tells the kids why he's brought them to an airplane graveyard in the middle of the desert to save them, and because of his caginess, some of the kids (ahem, Roland) suspect that he's actually a butcher, having them secretly unwound and sold on the black market. One of Roland's reasons is that the Admiral has perfect teeth, which he suspects are unwind implants.
Roland couldn't be more wrong, though. The Admiral was actually one of the first people to have his child, Harlan, unwound, and he's felt guilty about it ever since. So the Graveyard is part penance—saving kids when he couldn't save his own—and part recovery program. Whenever he finds a kid with one of Harlan's body parts, he sends them to his home as part of a big family reunion of sorts. As he tells Connor, he is "making things right […] bit by bit" (5.34.225). Literally.
After having traditional heart surgery (declining an organ from an Unwind), the Admiral returns home and is reunited with all the people who possess a part of his son. His good deeds pay off.