Generally, spyware is any computer technology that gathers information about a person without their knowledge.
It can be as simple as the "cookies" on your system (which you usually know about) to programs that you put on your system (or network) to see what others are doing on your system to virii sent from outside sources.
A cookie identifies your computer to websites, but they can also be used to find out where you have surfed.
Spectre and GurlWatcher are programs you put on your system or network to see where others have gone or what they have done on the system. Some of these will even email you with the results.
Some ad supported software has spyware to allow the software owners to know your surfing habits for marketing purposes.
There is spyware that some send with virii to get control of your pc.
It's a fairly broad term. IMO, most associate it with adware. And there is a lot of debate about people's privacy with spyware around.