What does this idiom cats coughed up fur ball mean?

That's not really an "idiom."

Cats are animals.

Cats lick themselves.

In the process of licking themselves they often swallow a certain amount of fur.

This hair gets balled up in their stomachs, and sometimes they'll cough (actually, it's more like "vomit") one back up.

The product of this is a "cat's coughed up fur ball". Like I said ... not really an idiom.