Spyware isn't viruses or worms, in that it generally won't copy itself to other computers, and it has a thin veil of legality in that you usually installed it, although you probably were tricked into it or it snuck in with some other program. Often it includes keyloggers or watch websites you browse, and it usually show ads. Basically it does whatever unethical thing will get the company that built it paid.

Sometimes spyware is installed on purpose, by other users of the computer, or on company computers. (There may be legal issues involved in removing the later.) The various governments sometimes also uses spyware, specifically keyloggers, to conduct legal 'searches' of computers, and there is a debate going on right now about whether spyare scanners should detect that. The debate was rendered mostly moot by heuristic scanners that detect all keyloggers.

Spyware is also called adware or malware. The best term is probably malware, meaning 'bad software', but we will continue to use spyware for historical reasons. Just be aware all spyware does not actually 'spy' on you, although a large percentage does in some way.