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The Council of State is the collective group of officials that make up the state's executive branch of government and it is provided for under Article III of the state constitution establishing the executive branch. Members of the Council are elected officials, elected by voters in statewide elections every four years and they serve four year terms until the next election.
Today the Council of State consists of the elected heads of the of the executive branch: Attorney General, Commissioner of Agriculture, Commissioner of Insurance, Secretary of State, Secretary of Labor, State Auditor, State Treasurer, and Superintendent of Public Instruction.
(The Council of State is not the same as the governor's cabinet. The cabinet is composed of other agency leaders that are appointed by the governor. These include the heads of the departments of: Administration, Commerce, Natural and Cultural Resources, Environmental Quality, Health and Human Services, Public Safety, Revenue, Transportation, and Military and Veterans Affairs.) You may also be interested in this NCpedia article on the Executive Branch: http://www.ncpedia.org/government/state/executive
The Council meets periodically, chaired by the Governor. It has a number of powers, including the authority to call for additional legislative special sessions (outside of the normal legislative calendar) and the power to make decisions about selling state property and taking on loans. You will see these briefly specified in Article III of the state constitution: http://www.ncga.state.nc.us/Legislation/constitution/article3.html
You may also be interested in this historical research report from the NC Office of Archives and History on the subject of the Council of State: http://digital.ncdcr.gov/cdm/ref/collection/p16062coll6/id/12822. It includes a compilation of various activities and decisions of the Council over time.
I hope this helps! Please let me know if you have additional questions.
Kelly Agan, Government & Heritage Library