Spyware is software that a website/manufacturer/organisation/game etc... etc... installs on your computer without your permission.
It basically does what it says on the tin : It spys on you and your movements.
It illicitly sends information such as your web history, the websites you've been to today, the setup and organisation of resources in your computer, the contents of the root directory of your hard drives, Windows version, computer specifications, name, address, phone number (if you have put it into the PC) and a whole host of other stuff to the servers of the people who own the spyware. They do with it what they will.
It's iniquitous, intrusive and should be bloody well illegal.
You can get spyware removal tools from people like www.lavasoft.de
. Their one is called AdAware and is very effective.