If you are in a car accident, you vehicle may suffer damage. If you sue the other driver and they have to pay you because it is their fault, then you receive damages - which is just another way of saying compensation for damage that you (or your property) has suffered.

Damage is singular and damages is plural. However, 'damage' is generally used more - "what kind of damage is there?" "how much damage has been done?" "Damages" tends to be used more in the context of the law - e.g. "___ is pursuing for damages done."