A virus is a program that is typically written to do damage to computers, mobile devices, networks and machines. It is always written in a way that it has the ability to spread fast and stay ahead of anti-virus programs for a short while. It reproduces by messaging, software inclusion and network crawling, sometimes it disables an anti-malware program before releasing it's malicious payload. Some viruses alter other files but a lot of them delete or cripple core system files making the host machine unoperable, sometimes while reproducing itself through a (local) network.
Virus hoax
A virus hoax is a kind of message going round which warns about a virus or contains some other type of untruth, but always with a character of urgency and severity. They often ask to resend the message to as many people as possible to warn them about the dangers as well. We also know virus hoaxes that ask people to delete certain files because they are installed by hackers or are very dangerous vulnerabilities. These messages never mean to do any good, most often they are being spread to do harm, sometimes to harvest data like "what was your first dogs name?", which can be a secret question too to reset your password somewhere.