In order to process PHP web pages, the webserver needs to route the source page through the PHP parser/compiler. It parses the PHP portions of the page, compiles it, and executes it, adding any output from it to the http output that is sent to the browser as an HTML page. This parser/compiler is what you would download if you want to run PHP web pages on your PC. You also would need to have a webserver set up on your PC. A fairly painless way to do this is to download and install the XAMPP package, which installs Apache websever and MySQL along with PHP.
As far as your web host, you'll have to check with them to see if they support PHP (and MySQL or other database system if needed). A quick way to check is to create a file on your web site with a ".php" suffix (such as "test.php") and have just the following as the contents:
If, when you access that page from your web host, you get a page with all sorts of info about the PHP installation, then PHP is installed and configured on your host. If all you see are the above lines of code, then it is not.