HTML and PHP are serve two different functions. HTML is for layout and PHP is a programming language.
For php to run you need a web server running php (and mysql for a database driven directory - almost all of them). Once you know you have both of these technologies installed on the server/hosting account then you can run a php directory. For the webserver to know to use php, the file using it has to have a .php extension and the php code has to be wrapped in php tags (i.e. <?php and ?>).
Your php/html page (index.php) may look like this:
Code:
<html>
<head>
....
</head>
<Body>
<?php some php code ?>
</body>
</html>
From that you can sort of see how HTML helps format the output of the php code. Any php page will have HTML on it. Almost all webpages are HTML pages, but some use programming languages to add functionality like this website.
If you wanted you could run your directory in a folder on your site like this: yoursite.com/directory/.
I hope that makes sense, post any questions if you have them.