A persistent world (PW) is a multiplayer module that runs continuously with plots and events evolving as time passes. They often fit into game type categories like "story", "roleplay", "action", etc.
All persistent worlds are run by players of Neverwinter Nights. BioWare was interested in the potential of persistent worlds, but they chose to take Neverwinter Nights in a different direction and never had official plans to develop a persistent world. Instead they provided tools (primarily the Toolset) and saw what their fans would come up with.