A computer virus is a small program which is designed to spread from one computer to another (hence virus) and to interfere with computer operation.  This can range from ejecting your CD drive to more severe consequences such as deleting or corrupting data, using your email application to spread itself and hence infect other computers, or even to erase everything on your hard drive.

History

The first computer virus, the "Creeper" virus, was first detected on ARPANET which was an early version of the internet as we now know it.  It was first identified in the 1970s and could use any modem to dial out to other computers and infect them.  It would display the message "I'M THE CREEPER : CATCH ME IF YOU CAN".  Some have suggested that another program which was released soon after, known as the "Reaper", sought out the Creeper and deleted it - some suggested it was written by the same person after experiencing regret at his or her action.

Transmission

A true virus can only spread from one computer to another when it is transported to the target computer, such as by sending over a network or the internet, or via removable media such as USB pen drives, floppy disks or external hard disk drives.

The most common method of spreading viruses nowadays is through email applications, where the virus is either an attachment to the email or relies on the user clicking a link in the text of the email.  This can also occur via instant messenger applications. 

Some viruses are spread through downloads from the internet, which can be hidden within illegal software or packaged with other files which you might download.