Include a partial template
You can't do relative paths, all paths must either be from the Drupal root or based on the namespaced path to your 'templates' directory: https://www.drupal.org/node/2143557.

I would avoid "from the Drupal root" and use namespaces, at least until https://www.drupal.org/node/2291449 is resolved.

{% include '@mytheme/parts/footer.html.twig' %}



  Edit: If you want to pass additional arguments for loop or for
  checking some vars to your included twig template you should write
  in this way:


{% include '@mytheme/includes/form-block.html.twig' with {dog: true} %}


Edit: Now that https://www.drupal.org/node/2291449 has been committed you can also do:

{% include 'footer.html.twig' %}


See https://www.drupal.org/node/2369981 for why you saw the file name as a string instead of a helpful exception.