There are three primary types of damages that may be awarded in a tort case: compensatory, punitive, and nominal.
Compensatory damages are intended to make the plaintiff whole again by providing reimbursement for financial losses incurred as a result of the defendant's actions. This could include medical expenses, lost wages, property damage, and pain and suffering. In some cases, compensatory damages may also include future losses that can reasonably be expected to occur as a consequence of the injury.
Punitive damages go beyond compensation, and are instead designed to punish the defendant for particularly egregious behavior. These are not available in every type of case, but may be awarded when the defendant's actions were wanton or reckless. The hope is that by imposing significant financial penalties on such defendants, they (and others) will be deterred from similar conduct in the future.
Nominal damages are a small sum awarded when there is no proof of any actual monetary loss suffered by the plaintiff. This might happen when there is clear evidence that the defendant committed a wrong but no evidence that this resulted in any quantifiable harm to the plaintiff. Nominal damages serve both to recognize that an injury occurred and to deter future similar injuries even when no other remedy would be appropriate.