In book VI of the Iliad, Hector says goodbye to Andromache and his infant son, Astyanax, as he heads off into battle. Andromache is an exemplary woman in her society, being a dutiful and caring wife to Hector. For example, she weaves him a cloak and prepares a bath for him as he has asked her as she awaits his return from battle (tragically, he will be killed). She is also a loving mother to Astyanax, which Hector acknowledges as he takes the very young child from the servant and hands him to Andromache.
But "precious" means more than simply that Andromache is a dutiful wife: it means that Hector loves her. This heightens the agony at his having to go into battle and risk death. Although he feels he has no choice—as he says to her, being a warrior is all he knows—the story here reveals the price of warfare. Homer shows us Hector, Andromache, and Astyanax as a family. In a tender moment, when Astyanax cries in fear over seeing his father in a metal helmet with a waving plume, Hector and Andromache laugh, but then Hector takes off the helmet and shows that he is more than a heroic fighter: he is a loving husband and father.
Homer thus critiques the warrior society that he also depicts as heroic: the cost of war is real and heavy, tearing a husband from his precious wife and leaving his beloved alone in the world after his death (her young son is also killed), reduced to a spoil of war.