How can a description be added to the body field summary widget in node edit form?
I assume you're using Drupal 8.
Try the below in your hook alter. This also assumes the usage of the default body field in use:
use Drupal\Core\StringTranslation\TranslatableMarkup;

// Ensure summary field existence.
if (isset($form['body']['widget'][0]['summary'])) {
  $form['body']['widget'][0]['summary']['#description'] = new TranslatableMarkup('Your summary description goes here.');
}