A victim impact statement is pretty much just what it sounds like. It is a statement in which the victim of a crime is allowed to communicate with the court regarding the impact that the crime has had on them. The statement can be given in writing or in person. This is done after the defendant has been convicted but before he or she is sentenced. This allows the impact statement to be considered when the sentence is being set.
Many states allow victim impact statements for a number of reasons. They feel, first of all, that the other parts of the system do not allow much of an opportunity to give information about the way in which the crime has affected the victim. Second, they give the victim a way to find some psychological closure -- the victim gets a forum for his or her feelings about what happened. Finally, these statements can offset statements by the defendant about why he or she should be treated leniently -- if you're going to consider mitigating factors in the criminal's life, you should also consider the harm they have done to their victim.