The red color of the costumes worn by the Handmaids symbolizes fertility, which is the caste's primary function. Red suggests the blood of the menstrual cycle and of childbirth.
The Handmaid's Tale argues that legally controlling women's reproductive freedom is morally and politically wrong. The suffering of Offred and the other Handmaids is directly caused by the Gileadean state's desire to own and control women's fertility.