Why call javascript behaviour within its own function? Looking at the JavaScript below, what does calling the behaviourName do? 

  Drupal.behaviors.behaviourName = {
    attach: function (context) {
      $('.someClass', context).once('some-handler').behaviourName(); // what does this do? 
    }
  };


I though that the behaviourName was generally used for name spacing. I can see in the site that im working on that the behaviour name is normally called within itself like in this example. What is this for?
You're reading that wrong - the return from once() isn't Drupal.behaviors (it's a collection of jQuery elements), and Drupal.behaviors.behaviourName isn't a function that will do anything by invoking it, anyway. You would need

Drupal.behaviors.behaviourName.attach();


To get anything meaningful, but that's not synonymous with the code you're referencing.

So that code is not calling a javascript behaviour within its own function. It's calling a jQuery extension function on the elements returned from once(). Most commonly when code needs to do what you're describing in Drupal, you'll see Drupal.attachBehaviors(); instead.

What you have is a convention used by the developer who wrote the script, nothing more; you'll need to ask them for their motivation for doing so, and how/where they're attaching the $.fn functions of the same names as the behaviours.