Linux is a free (as in libre, not always as in gratis) kernel that, together with tools from the GNU project, forms a stable, high-performance, multi-user operating system.
Its advantages over Windows are mainly ideological; it's free, usually in both of the above senses of the word, and the license, the GNU GPL
, prevents proprietary implementations from screwing you over (Linux "companies" sell support, not Linux itself, for this reason).
It's also much more stable than Windows, owing to its stricter memory management, access controls, and hardware abstraction policy, and its networking performance is better since it's really meant more for servers than for desktop usage. Linux has finer-grained access control at the user and device level, though to be fair, Windows has had Unix-style file permissions since NT. Reboot times for Linux, however, are measured in months, and the only reason you should ever need to reboot Linux is if you installed a new kernel.
The disadvantages of Linux compared to Windows are mainly issues of ease of use. Linux is hard compared to Windows, mostly because it tends not to detect certain devices. This is a circular problem, because the drivers tend to be written only for Windows to begin with. It also, despite what the makers claim, *does* require some work at the terminal in most cases, and this will scare away most Windows users who never worked with Dos and the 9x series. It shouldn't, because the terminal is much more powerful and easier to use than Dos ever was, but it does.
The other main issue is that, while there are a few hundred different flavors, referred to as "distros," most of them suck. There are a few big, well-supported distros, and many are based on them: RedHat, which is popular in the corporate world, Debian, which is minimalistic and tough by itself but forms the base for the popular Ubuntu, and Slackware, which is the oldest maintained distro and is closest to the "original" Linux philosophy. There are also a few oddballs like Gentoo, which is for experts only (forces you to compile *everything* but does the annoying work for you and gives you incredible performance), and Arch, which is a minimalist hybrid of Gentoo and Slackware.
Save yourself headaches: newbies should use Ubuntu, experts should use Gentoo or Slackware, purists should use Debian, and no one should use RedHat or any RedHat based distro unless you're corporate and need it, in which case you want CentOS (RedHat for free with no tech support). Just be prepared to get your hands a little dirty, and to search the web and your distro's forums for help. There is always, always an issue that pops up that will never be in the manual or installation docs.
Most of all, remember that Linux won't insult your intelligence, but it won't hold your hand either. You can't always breeze through a Linux install like you can with Windows (though Ubuntu and friends are changing that), but you will get a solid, stable, and working system. Linux rewards effort and inquisitiveness, and punishes laziness.
Linux is about choice. That means you're free to use it, or not to use it, but it will always be here for you.