Okay, so, Linux is a free operating system as far as normal desktop users are concerned. There are hundreds of distros available, but since it appears that you're a noob when it comes to Linux I recommend you get Ubuntu (
www.ubuntu.com) - if you get it, that is.
There are stacks of things that are better in Linux than Windows, such as security - for a normal desktop user, firewalls and antivirus/malware software are totally unnecessary - and the fact that majority (all?) desktop distributions are free, and generally Linux seems more stable, but that may be just my personal experience. The main drawbacks (when compared to Windows) are that 1) it's harder to use, though Ubuntu (and several other distros) aims to make Linux as hassle-free as possible for beginners and ain't a lot harder to use than Vista/XP when you get your head around it and 2) Compared to availability of software for Windows, there is a lack of software for Linux in certain areas. However, there are equivalents of most windows-software for Linux, such as OpenOffice=MS Office. Unless you need very specialized software, you should be alright with Linux as far as software availability is concerned, though.
Based on my personal experience, it may be a little hard to get your head around a few things in Linux and some things may seem just downright scary if you're not literate with computers, but it's actually quite easy to learn and when you "get it" it's in many areas actually more convenient&easier to use than Windows. Also, bear in mind that to get the most out of Linux you need internet access - most distros seem rather "internet-dependent" and I personally wouldn't use Linux for computer that has no access to internet, unless all software you need comes with the distro.
Oh and also, while there are several great free games for Linux, generally there is a lack of Games for Linux. However, unless you demand Crysis-like graphics, the games that you can get for Linux should keep you busy.
Okay, that was a... "general introduction", not a good one and probably a bit broken but it gives a basic idea of what Linux is about.
As a last note, it IS possible to run Windows applications (and games) on Linux through an emulator, such as Wine, but I wouldn't use it since you have Windows, if there are no Linux alternatives for Windows apps you need you can always dual-boot i.e. have both Linux and Windows installed - you get to pick which one to boot at the start.
EDIT - if you want to try out Linux, you can install it on a Virtual Machine and see if it suits your needs.