The short answer is: Linux is the kernel of a free operating system that suits as a replacement for Windows or Mac OS. Both Windows and Mac OS are proprietary software and the user cannot modify how these operating systems work. The Linux kernel and the GNU applications that run on this alternative operating system are (usually) free of charge and free to be modified by the user or anyone with some development skill. It is built by the users, for the users. The operating system can be called GNU/Linux (to credit the work of GNU) or simply Linux. GNU stands for Gnu's Not Unix and Linux for Linux Is Not UNIX. These are called “recursive acronyms”. They are called UNIX-like systems because they were inspired by UNIX.
This short video was made by the Linux Foundation at the occasion of the 20th anniversary of Linux (1991-2011) to tells the story of it's development.
I must say that the main differences between a proprietary software and a free or open source software is more philosophical than really a matter of price or quality of the product. All these three operating systems are suited for most uses and have their own share of advantages and disadvantages. The choice is a matter of knowing what the differences are and picking the one that is right for you. A misconception about Linux is to think that only experts have the ability to use and appreciate it. This is not the case anymore. The learning curve for any of those operating systems are pretty much the same. As anything in life, the deeper you want to go the more you have to spend time on it.
As a matter of fact, Linux is all about choice and exploration. As opposed to Windows and Mac OS where you have only a couple of “flavors” (like family pack, 64bits or server edition), Linux are available in a myriad of so called “distributions” or distros for short. Once you have chosen to use Linux you still have to find your distribution of choice. Distributions are a sort of package that contains a number of predefined applications and drivers, organized in a coherent structure. But no matter what is the distribution you chose you can still customize it as much as you want (eventually creating your own Linux distro). Since the majority of them are free, you can test many before deciding which one suits you best. You can take a look at our article about the mainstream GNU/Linux distributions, or visit Distrowatch to have an overview of the various distributions available.If you are interested in GNU and Linux, don't take my words for granted, just download a copy and run it from a CD or USB key, try it out (without modifying your computer) and decide whether or not you want to install it. It's easy and fast. In a couple of hours you will have a real world experience of what I'm talking about! A great distro to start with is Ubuntu. Take a tour and enjoy computing in a new dimension!