Damage can be a noun and a verb 
If you damage something it means you harm or break it.
Damage is the harm you cause to something.
The computer was damaged because someone had dropped it in the factory.
The plural noun damages means compensation (money) paid by someone who has done something wrong to the person or company affected as a form of punishment. This is a legal term.
Fly By Night Ltd were ordered by the court to pay £70,000 in damages to Mrs Treacle for their behaviour towards her.