$('input.preview').on('click', function(e){
    e.preventDefault();
    $('#form').hide();
    category_id = $('#category_id').val();
    $('#previewArea').empty().html('Category: '+category_id).show();
 });

<div id="previewArea"></div>
<div id="form">
    <select name="category_id" id="category_id">
      <?php $res = mysql_query("SELECT * FROM `posts`");
      while($row14 = mysql_fetch_assoc($res)){
        echo '<option value="'.$row['id'].'">'.$row['name'].'</option>';
      } ?>
    </select>
</div>

<input class="preview" type="button" value="Preview">