Perhaps I can rephrase this question into asking what more it means than allowing there to be a fold in the hip such that leg is not in the same line as the torso.
Well, generally the admonitions are about how the body is relaxed but there are no "wrinkles" along the surfaces, so that it is hung as one unit; the hips and lower back are relaxed while the legs hold all the weight. If the hips are relaxed and the shoulders are relaxed but the overall 'connection' of the body is stretched (not tensed though) so that there are no 'wrinkles', the twisting one part of the body will spread lines of force easily to other parts of the body.
To give you an example, if you stretch your right arm out in front of you so that you give it that nikyo twist (as in the 4 wrist exercises) and the 'connection' is there (not too tight and yet no 'wrinkles' in the connection), the twist should easily convey up the arm over the back and to the kidney area on the right side; an even better relaxed connection will also be felt to the feet.
So the short answer as it refers to the hip is that the hip is relaxed and not under tension because the weight is sunk into the legs, not into the hips and lower-back, thus leaving the body relaxed and pliably connected.