Spyware is any program that's installed either without your knowing about it or as a fine-print inclusion with some other software, that usually gathers information about you or your computer and uses that information in some way that you didn't explicitly agree to. Programs like CometCursor and Gator install themselves in the background when you visit certain webpages, without even notifying you that they're doing it, and then they run forever until you remove them. Some programs record every website you visit and send that information to marketing companies. Some programs add banner ads or popups to various other programs (web browsers) on your computer in a way that you might not even notice. Some programs change your homepage to some company's website every once in a while without asking first in hopes that you'll buy their junk. I think some of the more malicious ones sit on your computer and try to make long-distance phone calls to other countries using your modem so that you get a huge phone bill.

Trojan horses or keyloggers would be worse. Trojan horses let other people connect to your computer and execute commands like they were sitting at your desk. Some let you take over someone else's mouse, so hopefully that's not what you have. Keyloggers record every keypress you make and email or otherwise send that information back to someone else in hopes of getting your passwords or other sensitive information.