Hi there.
MySQL is typically used as a database server. In other words, it stores information in databases and provides an interface through which PHP can connect and retrieve that information. A database, in simple terms, is basically information stored in tables. Of course, it's more complex than that, but that's the basic idea.
Consider an example of PHP and MySQL. Lets say Company X wants to have a website where customers can shop for the company's many products. An efficient method of storing product information (inventory) is by using a database. So, a database designer will design an inventory database for Company X. It might look somewhat like this:
Code:
Product ID | Description | Price | Cost
-----------------------------------------------
22939812 | a product | $9.99 | $4.00
(a real-life inventory database would have to contain more information, however)
So, the designer uses MySQL to create this database. He would create the inventory 'table' (as seen above) with the 'fields' of Product ID, Description, etc. A web programmer would then write a PHP script to retrieve this information from the server, using a script called SQL (structured query language).
Here's a MySQl intro website:
http://www.devshed.com/Server_Side/MySQL/Intro/
Cheers!