Open source is a generic computer term that refers to the availability of program code. A piece of open source software means that the program code is “open” to the public. WordPress is open source software.
With open source software, anyone can download the program, study it, change it, use it, and/or redistribute it to someone else all free of charge. Because open source software is available to a larger number of developers, open source software is often more robust because problems, bugs, and loopholes are quickly discovered and fixed (patched). Many people also believe that open source software is also more dynamic because it will get updated more often thanks to the larger number of developers.
The downside to open source software is that the original creators no longer hold exclusive copyright over the software and therefore do not receive any income when their software is used. In addition, because open source software is publicly available, malicious programmers may study it in order to take advantage of loopholes or security weaknesses. And because open source software is not sold by a company, it does not come with any warranties or legal protection for consumers.
WordPress has been open source from the beginning of its history based on a belief that being open source leads to more flexibility and responsiveness. For instance, there are tens of thousands of plugins developed by outside developers, most of which are available to site administrators for free, and this could not have happened if WordPress was not open source software.
Note: While WordPress is free (as in no monetary cost) to use, keep in mind that WordPress is protected by GPL (General Public License) copyright which comes with a number of restrictions, including the fact that any derivatives must also be given a GPL copyright.