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Like most software, WordPress is distributed under a license, which means there are certain things that you are legally permitted (and not permitted) to do with WordPress software and source code. WordPress is distributed under a license called the GNU General Public License, a very popular license in the open source industry. If that doesn't ring a bell, read on.
The GNU General Public License, or GPL, is an open source license. Open source doesn't just mean that you can view the source code — it has political and philosophical implications as well. Open source, or "Free Software", means you are free to modify and redistribute the source code under certain conditions. Free doesn't refer to the price, it refers to freedom. The difference between the two meanings of free is often characterized as "Free as in speech vs. free as in beer." The GPL is free as in speech.
The reasons for WordPress releasing under the GPL are both practical and idealistic. WordPress was born of the very freedom mentioned earlier. The predecessor to the WordPress project, b2/cafelog, was also an open source project.