Previously, when writing a simple settings form, it was common to use system_settings_form() to quickly save values into the "variables" table. Since all variables are deprecated in Backdrop and should not be used, system_settings_form() is deprecated as well. Now when creating settings forms, submit handlers must be individually written to save values into the respective configuration file.

Old:

function my_settings_form($form, $form_state) {
  $form['my_setting'] = array(
    '#type' => 'textfield',
    '#title' => t('My setting'),
    '#default_value' => variable_get('my_setting', ''),
  );
  return system_settings_form($form);
}

New:

function my_settings_form($form, $form_state) {
  $config = config('my_module.settings');
  $form['my_setting'] = array(
    '#type' => 'textfield',
    '#title' => t('My setting'),
    '#default_value' => $config->get('my_setting'),
  );
  $form['actions']['#type'] = 'actions';
  $form['actions']['submit'] = array(
    '#type' => 'submit',
    '#value' => t('Save configuration'),
  );

  return $form;
}

function my_settings_form_submit($form, &$form_state) {
  $config = config('my_module.settings');
  $config->set('my_setting', $form_state['values']['my_setting']);
  $config->save();
  backdrop_set_message(t('The configuration options have been saved.'));
}

For now, system_settings_form() has been moved to drupal.inc for sites with compatibility with Drupal still turned on.

Introduced in branch: 
1.0.x
Introduced in version: 
1.0.0
Impacts: 
Module developers
Theme developers
Related Github Issues: 
https://github.com/backdrop/backdrop-issues/issues/397