I can see some eyerolls out there via my psychic powers. "Oh, she's going to be talking about closed and open hips, how droll." You would be wrong. I've heard the terms, and I've had coaches tell me to hold my leg in a certain way and say "That's open." or "That's closed". Those coaches may know what they mean but I can break down the free hip position into SIX positions. Open and closed don't cut it for me.
So here's a picture of a dancer in what is (probably) an 'open' hip position:
Not to me. To me this is a hip in the back position, with externally rotated leg. Next up:
So here's how I've broken it down:
Hip position--Forward back neutral
Leg rotation--External neutral internal
FO3--Free hip in the back position, externally rotated.
FO edge--Free hip in the back position, neutral to external rotation
BO edge--Free hip in forward position, neutral rotation
FI3--Free hip in forward position, external rotation
Mohawk--Going in: Free hip in back position, neutral to externally rotated leg. As I bring the free foot forward to the arch of the I bring the free hip to the neutral position, step down and switch, bringing the new free hip into the back position with external rotation.
This is nothing you could explain to a child. But as notation it certainly is more reliable and descriptive than 'open' and 'closed'.
For me this has proved to be a life saver. Because I have one hip that is naturally back and the other neutral, I've had to struggle with 'sidedness'. By understanding what's going on in a detailed way in my free hip, I've seen a lot of improvement as I'm able to make adjustments based on my knowledge of my own body.