When a web page is accessed, the server checks the extension to know how to handle the page. Generally speaking if it sees a .htm or .html file, it sends it right to the browser because it doesn't have anything to process on the server. If it sees a .php extension (or .shtml, or .asp, etc), it knows that it needs to execute the appropriate code before passing it along to the browser.
The way to execute PHP on a .html page is to modify your .htaccess file. This file may be hidden, so depending upon your FTP program you may have to modify some settings to see it. Then you just need to add this line for .html:
AddType application/x-httpd-php .html