Damages awarded in excess of any actual damage or loss suffered by the claimant, for the purpose of punishing the defendant's conduct and deterring other potential wrongdoers. They normally supplement compensatory damages. Punitive damages are available in the US system but normally not in the EU.
For further reading on punitive damages: see for instance a book "Punitive Damages. How Juries Decide" by Sunstein, Hastie, Payne, Schkade, Viscusi; and a book "Punitive Damages and Business Torts" by Collin, American Bar Association.