Punitive damages refers to a very special case in law, where damages are awarded to a plaintiff as a means of compensation and/or deterrent to the defendant, preventing them from committing similar crimes in the future when it's deemed a high probability. Punitive damages may also be awarded to a plaintiff simply as compensation for actions they have taken that were related to the crime of the defendant and have put them at risk in some way. It should be noted that the primary purpose of punitive damages is not compensation to the plaintiff, but prevention of future crimes from the defendant - and that's the reason the plaintiff doesn't receive the entire sum either, and they're usually awarded only a percentage of it.
Punitive damages can be used in a variety of cases, and some jurisdictions even recognize it where a breach of contract is involved - however, these cases are special and require special examination, as punitive damages cannot be awarded in contract-related cases by default.
The possibility for demanding punitive damages so easily has lead to various extreme cases where large amounts of damages were awarded for seemingly absurd reasons, such as spilt coffee which was too hot (resulting in over $2 million being awarded in punitive damages) - this has lead to some reforms in the laws related to punitive damages, and it's not as easy to claim them in modern times as it was previously. However, it remains one of the most commonly exploited types of case in the judicial system.