Persistent layouts would save all objects/instances on that layout in their current state/position when you leave that layout.
For example, if you were to create a game like dragon warrior or final fantasy on the NES. If you walk into a dungeon from the main world, that dungeon could be its own layout. If you set the dungeon layout to be persistent, when you exit the dungeon and go back to the main world, it would save the position and state of the instances in the dungeon. Then, when you go back to the dungeon everything would be as you left it.