Well, there are multiple definitions of a "virus".
The most common one (and the one your students probably know) is basically a catch-all term for all malware, ex. "my computer has a virus!!!"
The correct definition of virus is a program that reproduces over a network, with human aid. It may infect certain files by appending malicious code, so that when the infected file is run, the virus is also run. When the virus is run, it runs code that spreads it to other computers, and also executes a payload. The payload is the part of the program that makes it malicious or not; some payloads are relatively benign, basically electronic graffiti (popping up dialog boxes with obscenities, for example), but others range from dropping other malware to stealing passwords and attempting fraud.
Viruses are commonly confused with worms, which do not require human aid to propagate.
Another kind of malware that a virus is confused with is called a 'Trojan Horse' (beware of geeks bearing gifts?) that pretends to be a useful program, such as a free antivirus software, but contains a payload.
I have to explain things like this all the time to my friends that are not exactly as technologically literate as some. What I do is ask them for their definition of virus, and then explain what the correct definition is.
(panicked n00b: THERE'S THIS NEW VIRUS THAT IS SPREADING UNCONTROLLABLY AND NO ONE CAN STOP IT!!! geek: no, that's a worm. Viruses can't spread on their own. [proceed into definition of malware in layman's terms])
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Two questions you might also want to look at for more reference material: How does a CPU know what the commands mean? and Can some software physically damage hardware?
– Breakthrough – 2011-08-10T17:34:40.2405A Virus is only one form of Malware, are you intentionally asking about a virus or Malware in general?, which encompasses all the other terms like worm, trojan, etc. – Moab – 2011-08-10T17:37:28.017
1Some people might be scared they get infected ;-) – Tomas – 2011-08-10T18:08:17.780
@Tomas Telensky actually that reminds me of when I was younger, and my grandmother overheard my dad talking about computer viruses. She told him, "Don't let your son go on the computer, I don't want him to catch a virus and get sick!!!" – Breakthrough – 2011-08-10T18:17:43.587
1"Comparing what a computer virus does to a real world situtation" — Are computers not part of the real world anymore? – jwodder – 2011-08-10T20:15:18.040
1@Moab All non-technical people may not be knowing what a "malware" is but they are familiar with the phrase "computer virus". This is because of the popularity of the word "anti-virus". My question is about Malware in general. – nixnotwin – 2011-08-11T01:02:15.610