UNIX is an operating system - or rather, its a range of operating systems maintained and distributed by numerous venders.
UNIX differs from Windows in many ways. There are, for example, no drive letters - everything is in one single hierarchy, and devices and network shares are "mounted" into directories underneath. The main focus is also on the command line, as opposed to the GUI, although the GUIs are getting better. There are a range of different GUIs available.
Popular UNIX variants include Solaris, FreeBSD and Linux. Linux is actually a complete rewrite of UNIX, released under a licence called GPL that means that the code is open source.
http://en.wikipedia.org/wiki/Open_source
Things UNIX does well:
Server stuff like databases, DNS, firewalls, etc.
Scripting languages
Development
Things UNIX does not do well:
Games
Multimedia
If you are interested in UNIX, the best way to get into it is to download either Solaris or Linux (probably Linux is best) and install it. You can either a) Install it onto a spare machine, b)Set up a dual boot with Windows (there are many posts on this site on how to do that, or c) Install it as a vmware image using (the free) Vmware Server
www.vmware.com
Once you have it installed (most UNIXes have installation processes just like Windows..) then you can start to explore it. Read up on how to use the shell -
http://partmaps.org/era/unix/shell.html - as this is how you do just about everything.