The Periphery was a region of space within the Galaxy, located at the galactic Rim slightly in the direction of Trantor. It was here where the First Foundation was located on the planet Terminus, and consequently was the political center of the Foundation Federation, when it was founded.
Imperial control was weakest in the periphery, as planet governors there frequently possessed their own fleets. Santanni revolted during Forward the Foundation. About 50 years after the First Foundation was established on Terminus, the emperor granted the periphery autonomy. This effectively removed them completely from Imperial control, making the dissolution of the Empire far more apparent than it had been before.
In the years preceding the fall of Trantor, the periphery became any area outside the empire as this area became larger the empire became less and less great.