The "old world" refers to the sphere as it was before the Peace Wind, before the Long Cold, and before the Great Whump--from where all modern accounts of time and history begin with the end of what came before and the start of the Avantsphere as we know it now.
There are many clues, hints, and stories scattered about the land in regard to what has come before, though no clear record has been established. Many people, such as the influential Beardsman Family, have made it their goal to unravel the mysteries of the past, in attempt to gain knowledge and power with what came before.
From the collective facts and robust theories put together, the people of the old world were of great mechanical and biological ability, some near supernatural to imagine today, with a great emphasis on invention near what would be the end of their times. We see this in the revived hulls used to fight The Last Great Air War and the generator-like silos that still power grids in across the sphere.
It can be difficult to tell what has grown and mutated with time in the current world and what remains from the past.
Most will mill about their lives without much care for the preclude to their existence, as it is seen as merely what happened a long time ago, but others still wonder what the old world was like.