That my new ballet teacher said this morning: Everything in ballet is either an action, a reaction, or a statement. There is no art without story." As someone who has been thinking a lot about story lately, this felt relevant.
From his demonstration and examples, one can see he is talking about having intention behind one's movements. He says "you can't just connect the dots, that's not saying anything," and he says, about footwork, points and kicks etc, that your have to have a destination, you should have a point you are aim to--
All this is about imbuing motion with intention--or you could say purpose.
In my screen analysis class, one of the first things we talked about was the definition of filmic action as being "purposeful movement toward an objective." In stories, characters have action, ie purpose, intent. On the dance floor, a dancer who operates with a sense of intent, of having an objective, that dance will feel to the audience like she has "character" not just a command of the choreography.