Yes, WordPress is open source. Open source is a powerful software development model that make the software source code freely available and provides for free licensing of the software for any purpose. Wikipedia, the online encyclopedia, says this about open source,
Open-source software (OSS) is computer software with its source code made available with a license in which the copyright holder provides the rights to study, change, and distribute the software to anyone and for any purpose. Open-source software may be developed in a collaborative public manner. Open-source software is the most prominent example of open-source development and often compared to (technically defined) user-generated content or (legally defined) open-content movements.
The open-source model, or collaborative competition development from multiple independent sources, generates an increasingly diverse scope of design perspective than one company development alone can sustain long term. And a report by the Standish Group (from 2008) states that adoption of open-source software models has resulted in savings of about $60 billion per year to consumers."
See this page for information about the General Public License (GPL) under which WordPress is regulated.