PHP
PHP is a full-fledged programming language that is especially suited for web development. Among other things, it can be used to simplify the maintenence of a web site.
Where PHP especially shines though is in its ability to pull information out of a database for use in a web page. This way, it is possible for the PHP application itself to generate web pages on the fly, useful for doing things like displaying products someone might be selling on a web page.
MySQL
MySQL is a widely used open source database. Most of the online stores you see are using either MySQL or something very much like it.