Although MySQL can be used for free and is open source, MySQL AB holds the copyrights to the source code. The company offers a dual-licensing program for its software: one allows cost-free use through the GPL under certain common circumstances, and the other is a commercial license bearing a fee. They’re both the same software, but each has a different license and different privileges. See http://www.fsf.org/licenses for more details on the GPL.
MySQL AB allows you to use the software under the GPL if you use it without redistributing it, or if you redistribute it only with software licensed under the GPL. You can even use the GPL if you redistribute MySQL with software that you developed, as long as you distribute your software under the GPL as well.
However, if you have developed an application that requires MySQL for its functionality and you want to sell your software with MySQL under a nonfree license, you must purchase a commercial license from MySQL AB. There are other scenarios in which a commercial license may be required. For details on when you must purchase a license, see http://www.mysql.com/company/legal/licensing.