Typically, what we usually call an Operating System, is a combination of software involving a kernel, whose job is to manage the resources of the machine and some applications that run on top of the kernel, called the userland (this contains browsers, compilers, pdf readers, anything that isn't the kernel, or a driver, or maybe a vm hypervisor).
The rest of this question can not be answered without some historical context. Richard Stallman anounced the GNU Project on the 27th of September of 1983. The aim was to provide the software needed to develop a UNIX like operating system (and the accompanying userland) as free software. By 1992, the GNU Project had completed nearly all pieces essential for their software - except for one: the kernel. By the same time, Linus Torvalds released his kernel Linux (version 0.12) as free software, licensed under the GPL license. So for the first time, it could be possible to run a computer comprised (nearly) entirely of free software.
Linux (as mentioned) is a kernel, and, although it's the ultimate base of the software that allows you to use your computer, it's not of much usefulness alone. You should pair it with some sort of applications (userland) for it to run. That's what GNU/Linux distributions like Debian or Ubuntu and the like do.
It's worth mentioning that a kernel is both important and unimportant at the same time. Allow me to explain. Most people that use a computer are accustomed with the userland rather than the kernel. The kernel is mostly transparent, and most people would use another kernel with the same userland and might not even notice the difference (unless of course they are depending on a feature provided by a particular kernel).
Therefore, when you use Linux, you trully are using a realisation of the GNU operating system; that is the Linux kernel and the GNU userland (GNOME, GNU Compiler Collection, GNU debugger, GNU Coreutils, GNU binutils, etc). That's why the FSF insists on calling it GNU/Linux (in my opinion, a fair request).
You can of course, use Linux without the GNU userland (hint: Android, Busybox) and ofcourse use the GNU userland on top of other kernels (kfreebsd, hurd, etc).
As for the Unix is open source and the like, that is a question that can involve quite a bit of arguing. You might however find some useful information here