Why Tags don’t appear in my page?

Run a loop to output your tags:

$posttags = get_the_tags($post->ID);
if ($posttags) {
    foreach($posttags as $tag) {
        echo '<a href="'.get_tag_link($tag->term_id).'" title="'.$tag->name.'">'. $tag->name .'</a>'; 
    }
}

You don’t have to provide $post->ID if you are using this inside a loop.