In a lawsuit, "damages" refers to 1) the harm an injured party suffers because of another party's wrongful conduct; and 2) the money awarded to one party because of an injury or loss caused by another party.
For example, in a personal injury lawsuit: the injured person (the plaintiff) usually sues a wrongdoer (the defendant) for "damages" including:
And if the plaintiff's lawsuit is successful at trial, the court will order the defendant to pay the plaintiff a certain amount in "damages."
There are many different types or categories of damages. See: actual damages, compensatory damages, general damages, punitive damages, special damages.