Edit in JSFiddle

<form class="sample_form">
  Mailing address differs from home address
  <input class="conditional_form_part_activator" type="checkbox" name="mailing_address_differs">

  <div class="conditional_form_part">
    some other content
  </div>
</form>
  .conditional_form_part {
    display: none;
  }

  .conditional_form_part_activator:checked + .conditional_form_part {
    display: block;
  }