In a legal case, punitive damages are the extra money that's awarded by a judge to punish the defendant and compensate the plaintiff.
Not every court case involves awarding punitive damages, but when a defendant's actions badly hurt another person or group of people, they are often punished this way. The phrase comes from this intent to punish wrongdoing, with punitive rooted in the Latin punire, "to punish, correct, or chastise." While punishment is the main goal, punitive damages also financially help people who were harmed by negligence or violence.