<?php
   $data = $_POST['content'];
   file_put_content('conteudo_do_site', $data);
   echo 'salvo!';
?>

$.ajax({
        type: "POST",
        url: "save.php",
        data: {'content': $("#content").val()},
        success: function (data) {
            alert(data);
        }
    });

<form action="javascript:sendForm();" method="post" style="border-radius: 10px;">
            <textarea id='content' name="conteudo">
                    <?php  echo file_get_contents("conteudo_do_site.html"); ?><!--Salva o que voce escreveu-->
                </textarea><br>
           <button type='submit' class="oi" >Salvar</button>
          </form>