Linux, per se, is just one small piece—the kernel of the whole operating system. It's the software that directly controls the hardware and which runs all the other programs. It is what provides files and networking and what separates programs from each other so that they can't damage each other.
However, the Linux kernel without any programs to run isn't of much use. So people collect the necessary software to make up an entire operating system—everything from the shells that execute commands, to the X Windowing System, to the C compiler, to text manipulation programs, and more—and package it up in a way that can be (more or less) easily installed on a computer. That entire package, based on Linux, is called a Linux distribution.