It being free is the main selling point, so to speak. But there is a lot more that Linux does and Windon't (couldn't resist using the old Genesis slogan).
Big thing for me was the fact it is malware proof. Viruses and spyware do nothing due to the different kernal structure (big word for how the system operates). Going to sites like the infamous goggle.com would be PC suicide on Windows, but Linux is unaffected.
It is also getting more and more user friendly. The GUI (graphical-user interface) is getting cleaner and you have less work to do than before to get everything to work. Old Linux versions required a lot of CLI (Command-line interface) work. Now, the CLI is something you never need to use.
Installation is easy. Install the .iso onto a CD. Reboot to CD. Most all versions are live CDs, which run the Linux OS from the CD, so you can try it out before installing it. You can see what works and what doesn't. If you don't like it, reboot to your old OS and all you are out is a single CD and some time.
Installation is very quick compared to Windows. 10 minutes and you are done most of the time. Windows can take 2-3 hours, before you update which will take another 2-3 hours. The most recent .iso generally needs only a few minutes to update after install.
Installing software is easier as well. With Windows, you have to google around and see if you can find something. Linux has a package manager which you can search on to find exactly what you are looking for. In need of a video editor, type "video editor" in the search and it will bring up a list of options. Just click the checkbox and then apply to install it. Much easier and safer than how you have to do it with Windows.
The only downfall is most Windows programs don't work. Most of the time there are alternatives you can use (all of which are free), but mainstream PC games are an issue. PC gaming is the only reason I keep XP around (it never goes online though).
Here is a quick story: A friend of mine was wanting to dual-boot (Like I do) XP and Linux and get rid of Vista (which was causing a lot of problems). We installed PC Linux OS (the version of Linux I use) and got everything going in about 10 minutes. XP however, took me and a friend (both of us being nerds/geeks) more than 10 hours to get running right. 60x the time and effort to get XP running compared to Linux.