Viviana, PHP is a server side programming language.
HTML and JavaScript are also programming languages but they run on your web browser - with PHP, since you are the 'client' in an interaction with a website those languages are called 'client side' programming languages.
PHP on the other hand runs on the server.
Take this forum for example; all these threads and posts are stored in some sort of files on VAF's server and when you open one of these pages, the PHP code behind these pages reads that data (posts and threads) and writes them inside these HTML templates and then sends them to your browser.
The PHP code also knows if you are logged in or not, it can track your location in the forums and a lot more.
Now you can imagine how much power and control this gives you!
It is very powerful actually, many big websites are written in PHP for example Wikipedia and Facebook.
So with PHP files they mean files that have PHP code in them. For example, if you look at your browser's address bar right now you will see "showthread.php" (it's a PHP file)

!
I saw in memocharts.com FAQ that they are asking that your hosting package should support PHP - so it would make sense that this is the language the company uses on their own site.