A victim is a person who has had harm done to them by a criminal act committed by a criminal.
In the context of the law, a victim can sue the criminals who commit criminal acts against them. However, criminals are commonly prosecuted by the government anyway; this typically happens through a District Attorney's office.
There are many different kinds of crimes, and there are many different types of victims. For example:
Criminals who commit crimes against victims are subject to arrest and prosecution. If convicted, they will face punishments in accordance with the severity of their crime.