Something that's scarred is beat up, showing marks of wear or injury. The scarred wooden floors in the old school show that generations of kids have walked on them.
The adjective scarred describes something that's been hurt and shows some physical evidence of it. Your battle-scarred tabby cat might be missing a few whiskers and have a couple of nicks in his ears, and your knees might be scarred from falling off your bike. You can even be scarred in non-physical but lasting and serious ways, like being emotionally scarred by a breakup or a friend's betrayal. Being scarred this way might make you more cautious in the future.