Virus is a term that is thrown around a lot. The easiest way to describe it is to think about your computer like the human body. A virus is an infection with varying degrees of severity. Some are just mild annoyances, eg. sluggish response, fever (overdriving to system to overheat it), … Some can be fatal, causing actual damage to hardware and software.
There are also varying degrees of contagiousness. Most viruses are attached to an executable file (exe), but they can spread quite easily by copying themselves into other programs or files as well, even over a network environment or by sending themselves in an infected email.