A kernel is a constituent part of a larger operating system -- usually, in Linux distributions, the larger operating system contains a base of GNU tools, which is why many people refer to the kernel as Linux as, and the overall operating system as "GNU/Linux" (although many people don't make this distinction).
People call Linux an operating system because they have to choose a name to refer to the overall operating system that is provided by the sum of parts. Linux is the lowest level component that is readily visible to the user, so it is natural that it would take on this name and role. People don't usually refer to GNU grep as "GNU grep", they usually just call it "grep" -- to many users, GNU tools are not as visibly tied together as the Linux kernel.
Richard Stallman is very insistent about having people call Linux "GNU/Linux", since it contains many GNU tools (the C compiler perhaps being the most critical). I'm not so fussed, and not many other people are, either.
If you want clarity, GNU/Linux unambiguously refers to the operating system (rather than the kernel). "Linux" is significantly more ambiguous out of context.