What does 駄目 Dame mean?

Dame means no good. It refuses, forbids and condemns, depending on what it is aimed at, and it comes from a board game.

The origin

In go, a 駄目 is a neutral point: a vacant intersection lying between two settled positions, which will be filled at some stage and will not change the score for either player. Playing there is permitted and accomplishes nothing.

That is an unusually precise metaphor for uselessness. Not forbidden, not harmful, simply without value, and the word carried that sense out of the game and into general speech.

What it does now

Three jobs. It condemns a thing as no good. It forbids an action, in which case English would say don't. And it refuses flatly, on its own, as a complete utterance.

The register is direct. It is not rude in the way an obscenity is rude, but there is no softening in it, which is why a parent uses it with a child and a subordinate would not use it to a superior without care.

The contrast worth drawing

Set beside daijoubu, which declines by asserting that everything is already fine, this is the blunt instrument. One refuses by leaving the refusal unsaid; the other refuses by naming the thing worthless.

Japanese is often described as indirect. It has both of these words, uses both constantly, and chooses between them by situation, which is a more accurate picture than any general claim about indirectness.

The go inheritance is larger than this word

Japanese has taken a quantity of everyday vocabulary from board games and from other closed practices, in the way English has taken a great deal from sailing and from cricket. Nobody saying a plan is no good is thinking about a board, exactly as nobody saying they are on a level playing field is thinking about football.

What the etymology gives is precision about the original sense. The word does not mean bad. It means it will not count, which is a colder and more specific complaint.