You need to put the id of each item inside form to indicate the item that will be deleted.
<?php
$all_favorites= unserialize($_COOKIE['favorites']);
echo '<table>';
foreach($all_favorites as $key => $value) {
echo '<tr>';
echo 'Post-ID = ' . $value . ' ';
?>
<form method="POST">
<input type="hidden" name="id" value="<?php echo $value; ?>">
<button type="submit" class="btn btn-default" name="delete">
<span class="glyphicon glyphicon-trash"></span>
</button>
</form><br>
<?php
echo '</tr>';
}
echo '</table>';
if (isset($_POST['delete'])){
$id = $_POST['id']; // do security checks (sanitize etc)
// unset post with $id from cookie
}
?>