A computer virus is a set of unwanted instructions that are executed on your computer resulting in a variety of effects.
Viruses can be rather docile, such as simply annoying the user with a sound.
You can't get the virus by just being online for by calling another computer or reading your e-mail. Viruses are made for a variety of reasons. Some viruses have been created by disgruntled employees that want revenge on a company's product. Others are created to destructively celebrate certain holidays and raise the voice of certain religious and governmental fanatics. Sadly, those that create viruses for the challenge are misdirected individuals making poor use of their skills.