... someone asked me this a couple of days ago. I thought it was a little bit obvious, but you do need to consider what is at stake here when dealing with viruses and spyware.
A virus is a software program that changes settings in your computer to stop you from using it properly. It loads itself when you login, it hides itself from the Task Manager, and it causes errors to appear.
Many virus writers make them to merely prove what damage they can do or to show off to others.
Sometimes viruses are used to import malicious software into a computer.
A spyware program defines a group of mailicious types of programs that take over your computer. For example, adware (advert-based, popups, calling high charge numbers with diallers). A new type is called "randomware", where the spyware encyrpts all of your files in My Documents. The offender informs you that unless you do not pay them for a decryption code, you will not be able to open your files.
Spyware "spies" on your computer, watching everything you do. It can also install fake software such as anti-virus or anti-spyware, encourage you to pay towards buying fake software, and can direct you to fake banking websites to install viruses. Spyware is very dangerous because the worst types can record everything you type in (password, banking details, account numbers, phone numbers, emails) and also search all your files for contact infromation. This information is then collected by the spyware program and the next time you connect to the internet, all that data is sent off to the offender.
Yahoo Online Protection - What is a virus?
Symantec Cybercrime website
If you want a really easy graphical introduction to learning about it, click the Symantec link above and under "Phishing and Pharming" and "Bots, Trojans and Spyware", click the Flash Demo.