/**
 * Form builder
 */
function mymodule_test_form() {
  // ...
 
  $form['#prefix'] = '<div id="test-form-wrapper">';
  $form['#suffix'] = '</div>';
 
  $form['refresh_button'] = array(
    '#type' => 'button',
    '#value' => 'Refresh',
    '#ajax' => array(
      'callback' => 'mymodule_test_form_refresh',
      'wrapper' => 'test-form-wrapper',
    ),
  );
 
  return $form;
}
 
/**
 * Ajax callback
 */
function mymodule_test_form_refresh($form, $form_state) {
  return $form;
}

Drupal 7