The license under which the WordPress software is released is the GPLv2 (or later) from the Free Software Foundation. A copy of the license is included with every copy of WordPress, but you can also read the text of the license here.

Part of this license outlines requirements for derivative works, such as plugins or themes. Derivatives of WordPress code inherit the GPL license. Drupal, which has the same GPL license as WordPress, has an excellent page on licensing as it applies to themes and modules (their word for plugins).

There is some legal grey area regarding what is considered a derivative work, but we feel strongly that plugins and themes are derivative work and thus inherit the GPL license. If you disagree, you might want to consider a non-GPL platform such as Serendipity (BSD license) or Habari (Apache license) instead.