A PHP file is just an HTML file with a different file extension, and with snippet(s) of PHP code included. In this case, the PHP code you're using is: <?php include"nav.html";?>
So the pages that you want to insert the navbar into need to be .php, because they're the pages with the PHP code. The file it is you're inserting can be PHP if you need it to be, but in this case it's just static HTML so you can leave the extension as .html (see in the code above it's nav.html, not nav.php). Hope this makes sense.
Why would you need to write the tags using PHP? Isn't it just static HTML?