Both were sacramental objects used during a yearly ritual commemorating the "Ruin," which though not overtly stated probably refers to an global epidemic or a nuclear holocaust. An intricately embroidered robe was worn by the Singer, who recounted the history of mankind through hours of chanting, while he grasped in his hand a "sacred" rod or staff.
During one of such incantations, Kira gets a glimpse of the Singer's ankles and sees to her horror that they are swollen and bloodied, being shackled together with a heavy chain. She realizes that the "staff" serves as a crutch so that the Singer will not topple over and collapse while performing the ceremony.
Both the staff and the robe are used to preserve a sense of social order and hierarchy as well as serving as a connection with the past. Ironically, they are also used to dissimulate negative aspects about the current community, in which the individual is sacrificed for the state.