Local government is how each Province manages itself. In short, there are two main members of a Local Government - the noble and the Councilor. These are the same people as the Province's Ruling Council representatives. The Local Government may appoint to itself nobles from subdivisions of the Province or create a local council.
Local governments can create legislation - often referred to as Acts or Edicts - applying to their Province, but it most comply with the Supreme Directive and all the Imperial Decrees and Acts of Council.