The Old Imperium was a term used to describe the Empire that was ruled by the Corrinos and later the Atreides.
The Old Imperium initially spanned the known universe following the Butlerian Jihad, which banned all mechanical thinking machine technology. After the death of the God-Emperor Leto II, humankind exploded across unknown space, away from the boundaries of the Empire during a time that is known as The Scattering. Thereafter, the term 'Old Imperium' fell into use to describe the difference between what was the Corrino/Atreides Empire and the rest of the known universe.
Despite the passing of several thousand years, parts of the Old Imperium were stil under the control of bodies that were once powerful entities. These included Leto II's Fish Speakers, some Great Houses, the Bene Gesserit and the Bene Tleilax.
The term 'Old Imperium' was also used as an historical reference to the Corrino/Atreides Empire during the time people were returning from the Scattering, approximately 1500 years after the death of Leto II.