How can I explain what a computer virus is to people who are not familiar with computers and programming?

I think that the similitude with biological system (from which the word virus has been taken from) is good.

Like biological viruses causes the cells behavior to be subverted, computer viruses do the same with computer programs.

They also have other similar behavior:

1. both computer viruses and biological ones are self-replicant
2. both can't live without an host system
3. both are made by small pieces of information (DNA versus Binary Instructions)

The word "virus" helps. Most genetic material is beneficiary, but some is dangerous. Similarly, most computer software is written for the benefit of the user, but a computer virus is not.

Note that I am using the colloquial usage of the word "virus" to refer to all malware. When describing things yourself, be sure to use the term malware to refer to malicious software. A virus is only one type of malware.

Don't go explaining all the different types of malware but rather the effects that they can have:

1. They send spam from your computer
2. They attack other computers from your computer
3. They slow down your computer's performance and internet connection
4. They will parse your addressbook and send spam to your contacts
5. They will upload your personal files to malicious entities, including your banking information and credit card details