How does a computer virus work?

Computer viruses are mysterious and grab our attention. On the one hand, viruses show us how vulnerable we are. A properly engineered virus can have an amazing effect on the worldwide Internet. On the other hand, they show how sophisticated and interconnected human beings have become.

When you listen to the news, you hear about many different forms of electronic infection. The most common are:

Viruses - A virus is a small piece of software that piggybacks on real programs. For example, a virus might attach itself to a program such as a spreadsheet program. Each time the spreadsheet program runs, the virus runs, too, and it has the chance to reproduce (by attaching to other programs).

E-mail viruses - An e-mail virus moves around in e-mail messages and usually replicates itself by automatically mailing itself to dozens of people in the victim's e-mail address book.

Worms - A worm is a small piece of software that uses computer networks and security holes to replicate itself. A copy of the worm scans the network for another machine that has a specific security hole. It copies itself to the new machine using the security hole, and then starts replicating from there, as well.

Trojan horses - A Trojan horse is simply a computer program. The program claims to do one thing (it may claim to be a game) but instead does damage when you run it (it may erase your HDD). Trojan horses have no way to replicate automatically.

Source(Which the first author forgot to recognize): http://www.howstuffworks.com/virus.htm