The concept of always turning left can be applied in so many ways. For example, you can turn left (a) on every count, you can turn left (b) whenever someone touches you, you can turn left (c) every time you are left alone. But turning left is the main (1) concept, and everything else you apply to it is a secondary (a,b,c) concept.
The concept could also be "cool" or your idea of the word. Or sexy, or sophisticated, or whatever it is. That's a bigger umbrella concept which constitutes a combination of concepts to work together. So let's take the idea of "cool" and break it down.
Batman is cool because he is: powerful, fearless, and merciful. (we'll make it simple)
If that is your concept there are many ways to approach this and there are variations but you have a framework of what you want.
Powerful; moves that command authority and can defend for what he believes in. (fighting moves, that one move where someone punches, you grab, and then bring them to their knees (corny but you get the point))
Fearless; not afraid of any man or woman. (maybe walks into a crowd full of criminals , or down an alley full straight towards his arch-nemesis.)
Merciful; giving people a chance even when they have wronged you. (maybe spares the bad guy's life.)
So these moves would make the person appear to be powerful, fearless, and merciful in your dance/story.
There are character concepts, story/situation concepts, setting concepts, move/visual concepts, and music/timing concepts but that will be for another post.