What is the difference between published and unpublished waypoints? While reading some articles about free route airspaces I found reference to two types of waypoints:


  Free route airspace (FRA) is a specified airspace within which users
  can freely plan a route between a defined entry point and a defined
  exit point, with the possibility of routeing via intermediate
  (published or unpublished) waypoints ...


My question is the following: What is the difference between published and unpublished waypoints? How are they created? When are they used?

Could you please provide me documentation/citations as well in order to have a complete overview of the topic?
Published waypoints are waypoints that appear on the charts and in the published navigation databases used by GPS navigators or FMSes.  They are referenced using the published identifier for the waypoint. Examples: TPA, ITAWT.  

Unpublished waypoints are waypoints created by the pilot.  FMS allow for the creation/entry of a waypoint by the pilot.  The waypoint is defined by one of the following:  


Latitude/Longitude
Place/Bearing/Distance
Place-Bearing/Place-Bearing


The pilot-defined waypoint can then be added to the flight plan.  

Here's a snip of how a waypoint is defined in an A320:  

  

As to when you would use it, the short answer is when you need to or want to.  A common example would be to deviate a short distance off an airway (maybe 5 or 10 nm) to avoid a temporary flight restriction.  You would just want to avoid the restricted airspace and using a published waypoint or waypoints would take you farther off your route than necessary.