The title of systems admiral was borne within the Imperial Navy by the commanders of systems forces. Systems admirals were sometimes known as commodores, although this latter title also had other usages.
Systems admirals were mid-level commanders within the Imperial military hierarchy: on the one hand, the systems forces that they led were subordinate components of the Fleets commanded by Fleet Admirals, mere fractions of full Sector Groups; but the same systems forces were also subdivided into several squadrons commanded by their own admirals, each of which was comparable in size to the small fleets that had been maintained at the Sector level before the Clone Wars.
Systems forces were not normally assigned to specific volumes of space within the sector; rather, they were built around force pools, groups of ships and personnel geared to a particular mission profile: force escort was designed to combat piracy, smuggling and low-level insurgency, while force technical services was charged with front-line maintenance and salvage duties. Elements of a systems force could thus be sent wherever their particular capabilities were required in the Sector, and as a result, systems admirals might find themselves commanding ships and squadrons light-years apart, in dozens of different star-systems - and having to reorganize and reassign these forces in response to ever-shifting demands. Their tasks were made no easier by the fact that HoloNet access was still often limited to larger command vessels, requiring them to use courier ships to retain contact with their forces.
Behind the scenes
The rank of Systems Admiral appears only in the Imperial Sourcebook, although there are occasional references elsewhere to Imperial officers as "Commodores". In this context, it is likely that both "commodore" and "systems admiral" should be interpreted as titles denoting a specific sort of command, rather than particular ranks in a graded hierarchy, and it is even possible that they could be borne by officers who did not actually hold flag rank: the specific rank equivalent to a New Republic Commodore in Imperial service is usually given as Commander, while Michael Unther appears to have served as the "Admiral" of a full Sector Fleet while holding a rank lower than Rear Admiral.