I am writing a wordpress plugin but I've got a problem. When Wordpress is exhibiting posts &lifier pages on the website, I would like it to skip that publish/page once the custom area show_publish equals (this can be a simplified example). How do you do that?

Please keep in mind that to a wordpress plugin, not really a theme, and so i can't just edit the theme to skip individuals posts/pages.

Presuming you would like the wordpress plugin to dedicate yourself all styles and all sorts of queries.

You should use something similar to

<?php
add_filter('posts_where', 'check_show_posts');
function check_show_posts($where) {
    global $wpdb;
    $query = "
        SELECT {$wpdb->prefix}posts.ID as ID
        FROM {$wpdb->prefix}posts
        INNER JOIN {$wpdb->prefix}postmeta m1
          ON ( {$wpdb->prefix}posts.ID = m1.post_id )
        WHERE
        {$wpdb->prefix}posts.post_status = 'publish'
        AND ( {$wpdb->prefix}posts.post_type = 'post' OR {$wpdb->prefix}posts.post_type = 'page' )
        AND ( m1.meta_key = 'show_posts' AND m1.meta_value = '0' )
        GROUP BY {$wpdb->prefix}posts.ID
        DESC;   
        ";

        $posts = $wpdb->get_col($query);
        if($posts) {
            $post_list = implode(',', $posts);
            $where .= sprintf(' AND ID NOT IN ( %s )', $post_list);
        }
        return $where;
}

Update: added if($posts) condition to see if the query returns ID's or otherwise.