add post meta front end edit

This code should be conditional first and then form output since you can’t use wp_redirect after headers are set and you are updating so use update_post_meta instead of add_post_meta.

Try:

    if( 'POST' == $_SERVER['REQUEST_METHOD'] && !empty( $_POST['action'] ) &&  $_POST['action'] == "edit_post" && isset($_POST['pid'])) {
    $the_post = get_post($_POST['pid']); 


    $the_post = array(); 
    $the_post['post_content'] = $_POST['description'];
    $the_post['data'] = array($_POST['data']);

    $pid = wp_update_post($the_post); 
    update_post_meta($pid, 'rating', $the_post['data'], true);

    $link = get_permalink( $pid );
    wp_redirect($link);
}

<!-- edit Post Form -->
    <div id="postbox">
        <form id="edit_post" name="edit_post" method="post" action="">
        <p><label for="description">Description</label><br />
            <textarea id="description" name="description" ><?php echo $post_to_edit->post_content; ?></textarea>
        </p>
        <!-- wine Rating -->
        <fieldset class="data">
                  <label for="data">data</label>
                  <input type="text" value="" id="data" size="60" tabindex="20" name="data"><?php echo (!empty($val = get_post_meta($post_to_edit->ID,'rating',true))) ? $val : ''; ?></textarea>
        </fieldset>

        <p align="right"><input type="submit" value="Edit" tabindex="6" id="submit" name="submit" /></p>
        <input type="hidden" name="action" value="edit_post" />
        <input type="hidden" name="pid" value="<?php echo $post_to_edit->ID; ?>" />
        <?php wp_nonce_field( 'edit-post' ); ?>
        </form>
    </div>

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