What exactly does the next action mean?

Well, the next action is the next physical action you need to do to in order to move the current situation to completion.

Some examples :

• Talk to David about the book we need to buy (improve competence)
• Call Vanessa to schedule a meeting for marketing activities next month   (marketing campaign july 2009)
• Make a mind map for items to blog about  (update my blog)

These actions are real physical actions that need to happen. If I do them, I will move forward to completion (of a project).  (an example of a project is written between brackets next the the next action in the list above)

The basic idea is that a project exists of more next actions, but everything (or every project) needs a (one)  next action to go forward to become completed.