How are .inc files actually utilised in a module?
There are multiple ways .inc files can be included.

Hooks in general should all be included in the .module file, as that is the only file loaded on every page load by default, and hooks should always be available. However, hook_hook_info() can be implemented, telling Drupal that the hook should be looked for in another file. For example:

function hook_hook_info()
{
  return array
  (
    // Tell Drupal to look in a different file
    // for hook_form_alter:
    'form_alter' =&gt; array
    (
      // Tell Drupal to look in MODULENAME.forms.inc
      // for hook_form_alter:
      'group' =&gt; 'forms',
    ),
  ),
}


Next, you can use hook_menu() to look for a callback in an .inc file:

function hook_menu()
{
  $menu['some/path'] = array
  (
    ...
    'file' =&gt; 'includes/some_file.inc',
  );

  return $menu;
}


The same can be done with hook_theme():

function hook_theme()
{
  $themes['some_theme_hook'] = array
  (
    ...
    'file' =&gt; 'includes/some_file.inc',
  );

  return $themes;
}


.inc files can also be directly included with module_load_include():

// The extension is given in the first argument, and
// left off the last argument:
module_load_include('inc', MODULENAME, 'includes/some_file');


Though in forms, form_load_include() should be used rather than module_load_include():

// The extension is given in the second argument, and
// left off the last argument:
form_load_include($form_state,'inc', MODULENAME, 'includes/some_file');