It's having royalty as a member at some point in the club's history, then being granted the royal title as a result. I believe this is discretionary, not automatic, and it is also possible for the royal title to lapse if the club loses it's royal connection for a long time.
My club was royal due to having a royal member a hundred years or so ago, so they invited Prince Andrew to become an honorary member just to make sure the royal status didn't get revoked.