Like most software, Piwigo is distributed under a license, which means there are certain things that you are legally permitted (and not permitted) to do with Piwigo software and source code. Piwigo 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.
About the GPL
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.
What About the Price?
In addition to the freedom given by the GPL license, Piwigo is free of charge. You can download and use it for free. There is no trial version, limited in time or features.