PHP will work with virtually all database software, including Oracle and Sybase but most commonly used is freely available MySQL database.
Databases are useful for storing information categorically. A company may have a database with the following tables:
If you don't have a PHP server with a MySQL Database, you can download it for free here: https://www.mysql.com
MySQL is the de-facto standard database system for web sites with HUGE volumes of both data and end-users (like Facebook, Twitter, and Wikipedia). Another great thing about MySQL is that it can be scaled down to support embedded database applications. Look at https://www.mysql.com/customers/ for an overview of companies using MySQL.