The structure of $config_directories used to look like this up until 8.0-alpha7:
$config_directories['staging']['path'] = 'config_HASH/staging';
The implementation then enforced that this is a relative path within sites/$site_name/files, without respecting the public_file_path setting.
To specify a path outside, a path like ../outside_files/...
had to be used or the absolute
property set to TRUE.
The structure has been simplified to contain the relative path starting from the drupal root directory, just like the public files path too.
Configuration "staging" directory now moved to "sync" changes the example.
It looks like this now:
$config_directories['sync'] = 'sites/default/files/config_hash/sync';
That makes it more intuitive to use an absolute path or a path outside of the files directory (e.g. to have the staging directory in a version-controlled directory)
Note: Since #2161591: Change default active config from file storage to DB storage, the active configuration is no longer stored in the filesystem by default.