First of all we need clear about Kernel:
A kernel is the most important element of an operating system. For an OS to work, it needs a kernel. The task of the kernel is to handle hardware resources (memory allocation, disk access, device usage...). It sits in between the hardware and the software being executed.
An operating system is something that includes a kernel plus quite a few lower-level "applications" to allow you as a user to do useful stuff with your computer (think file manager, control panel and so on).
If I Strictly speak, Linux is not an operating system, it is a kernel. Although it is very common to call any Linux-based operating system as 'Linux'. GNU/Linux is the operating system that combines the Linux kernel and GNU software. GNU alone is not (quite) an operating system either because there is no functional kernel. The GNU project developed a kernel called HURD but it is not stable enough to make of GNU a complete OS.
What most people call “Linux” is often a “GNU/Linux” OS.
For example: Debian, Ubuntu or Fedora are GNU/Linux operating systems. Android, on the other hand, is an OS that is based on Linux (the kernel) but it is not a GNU/Linux OS... and nobody calls it Linux by the way.