The significance of Cafiero's family home in Barletta for his recovery was that it provided a familiar and comforting environment that helped him regain a level of lucidity. According to sources like Wikipedia and Libcom.org, moving to his family home seemed to have a positive effect on his health, as he responded well to the familiar surroundings of his youth. This indicates that the family home played a crucial role in his recovery process by offering a stable and reassuring atmosphere.