How does Apache MySQL and PHP work together?

MySQL

Let me answer from less 'technicall' point of view.

Apache is the HTTP server. It gets the HTTP requests and answers with the HTML code. PHP is used to generate this HTML dynamically on server side. MySQL is used by PHP for getting the data.

Once the Apache HTTP server gets the request for the page with php (or php3, php4, phtml or whatever is configured in Apache's config file), it calls PHP interpreter to generate HTML. Then this HTML is returned to the client - internet browser which sent HTTP request.

PHP has got an access to MySQL DB via several APIs. This simply means, that you can just call some function in PHP script to select, import update or delete some data in a table of DB. You can also maintain the DB, create, delete new tables a.s.o. There is a lot of functions for that ;)