The Administration was head of the civil wing of the Terran Federation -- the administration ran and controlled the day-to-day life of those within the Federation. In theory, the Administration also had some control over Space Command, though some -- such as Trooper Par and Supreme Commander Servalan -- would frequently act without their clearance. Some actions, however, were too important to take without permission from the High Council. Nevertheless, ships like the London were required to have permission from the Administration before they could even take flight into space.
In general, the public had great faith in the Administration. This was, of course, largely due to the fact that much of the population was being drugged into complacency on a regular basis.
The Administration is derived from Blakes 7.