Compensatory damages are damages meant to compensate you for your losses. These damages cover actual economic losses, like medical bills and lost income. They can also include compensation for pain and suffering and loss of enjoyment of life. The purpose of compensatory damages is to put you as nearly as possible back in the position where you would have been if the defendant’s negligence had not occurred.
Punitive damages, on the other hand, are intended to punish the defendant and to discourage others from engaging in the kind of negligence. An award of punitive damages requires a showing of something more than mere negligence.