What do we mean when we say it today?
We hate to burst your bubble, but this phrase has nothing to do with Charles Dickens. While he did spawn another word (Dickensian) into life, he didn't have anything to do with this phrase. Come to think of it, it might be a little weird to use your own last name as an explicative.
People say "what the dickens" today any time they are puzzled or surprised. We even say something "hurt like the dickens" sometimes. That's just taking the same euphemism and running with it.
It's a nicer way of saying a much stronger explicative. You can say this around your grandmother and she won't threaten to wash your mouth out with soap.