Any program that collects information behind your back in called spyware. They usually monitor your surfing habits, etc and then 'phone home' (they send that data back to authors) so they can then serve up ads to annoy you.
A lot of spyware files like to hijack IE hompages and other settings and other settings. So if you find your homepage is some strange website you've never heard of, then you've got spyware. Spyware files like to use up ram too, so if your PC is acting slow for some reason, you probably have spyware.
Download either Spybot S&D or Ad-aware (or both!). These programs will trawl your PC for spyware and remove the god forsaken crap. These programs are like antivirus software - they are only as good as their last update. Make sure you update 'em reguarly and scan reguarly.
BTW - Spyware is usually bundled with other software (Kazaa being a prime example) and if you remove it, the program it came bundled with won't work.
Basically, if you get asked, don't install any optional sponsors and try to stay away from crappy trial programs from people/companies you've never heard of.
Is there such a thing as Mac spyware? I mean, I know such a thing could be made, but is it common? Is there a lot of Mac shareware/freeware out there with bundled spyware?