How to do Basic URL Rewrite Without Redirecting

If you just want to see the content of the /hello-world post on /rewriteme page you can try to add something like this on the page.php of your theme:

<?php
    if (is_page('rewriteme')) {
        // query for the about page
        $your_query = new WP_Query( 'postname=hello-world' );
        // "loop" through query (even though it's just one page) 
        while ( $your_query->have_posts() ) : $your_query->the_post();
            the_content();
        endwhile;
        // reset post data (important!)
        wp_reset_postdata();
    }
?>