The Daiamid was a governing council and unifying authority on Kharak that held the Kushan kiithid together in the aftermath of the Heresy Wars. The name also refers to the building which housed the council, located in the Kiith Naabal city of Tiir. Following the Exodus a new Daiamid was constructed in the Hiigaran sector of Assam Kiith'sid, within which the New Daiamid held sessions. Occassionally this new council was simply called the Daiamid.
The Daiamid had its roots in the way in which Kushan kiith-sas on Kharak called together the senior members and leaders of their kiith as well as the vassal families within it. These representatives of a kiith's various members helped advise a kiith-sa on their decisions during war and peace alike. It was this that served as an inspiration for Iifrit Naabal-sa, the revolutionary who brought an end to the devastating Heresy Wars when he was considering a world government for Kharak.
His proposal was to allow each kiith to send its leaders and/or representatives to a single council where their suggestions, complaints, and pleas could be heard and resolved peacefully. Made up of all the sovereign kiithid of Kharak the Daiamid, at first a noble experiment, succeeded to become Kharak's government until the planet's devastation by the Taiidan during the Homeworld War. In Deserts of Kharak, this government is known as the Coalition of the Northern Kiithid, and is how the Kushani found the Guidestone to begin with.
It is unclear however how much power the Daiamid actually had. It was not until the Mothership Project that a global security force was actually formed, to protect Kharak's space program from sabotage by the rogue Kiith Gaalsien.
This internal weakness was observed after the Hiigaran Landfall when the New Daiamid, modeled after the old Daiamid on Kharak, began to have probelms maintaining unity.
The Daiamid is made up of the leaders of the kiithid. Kiith-sas of sovereign kiithid are recognized in the Daiamid as representatives of their kiith and speak for them and make laws on their behalf. Together these kiith-sas divide the power more or less between the larger kiithid. The Daiamid's representation it seems is partially based on population as well since in the years after the Hiigaran Landfall many kiithid were left powerless by lack of numbers, leaving only a handfull of kiithid with real power in the Daiamid.
The Daiamid is also headed by a leader elected by that body, known as the Sa of Sas. This leader appears to preside over the Daiamid although whatever real power they hold seems to be debateable. It is likely they are more of a legislative referee than anything more powerful, as a single leader heading the Kushan seems to be outside the cultural context of the kiithid.