This is a good question. A true computer virus has two qualities. First, it is a computer program that latches onto a computer to harm it. Second, it has the ability to replicate itself onto other computers and grow. The second quality is important to underline, because there are many programs that harm a computer (malware), but they are not technically viruses, because they cannot replicate.
If you think about a virus that humans get, it will be helpful.
As for anti-virus, it is another program installed on a computer and it does two things. First, it protects the computer from viruses getting in. Second, if there is a virus, it locates the virus and removes it. All computers should have some virus protection.