If a faction is the only faction with a System in a sector, that faction is said to have sovereignty in that sector.
If a faction has sovereignty in a sector they can do the following things:
Block the use of any non-combat object in the sector. This includes blocking the use of holonet relay stations, hyperspace lanes, etc. The owner of said object still has to pay upkeep.
Block the construction of any object in their sector. This includes blocking the construction of holonet relay stations, outposts, space habitats, the scanning of outpost sites, etc.
Block the passing of any non-combat object through the sector. This includes blocking trade fleets, survey fleets, etc.
If multiple faction have a system in a sector or if factions share a system, the construction, passage and use can only be blocked if all factions block it. This means that multiple worlds might want to come to an agreement on how to handle such things.