'Hanging Off a Step'...I don't get it

This is a ‘pelvic list’, or standing on one leg. It’s to build lateral hip muscle strength (you need this, btw. and you probably don’t have it). You can do slow reps, up and down. Or you can push down into the standing leg and hold it. Both will work the right muscles. Here’s some pointers:

Your legs must both be straight and vertical. Don’t bend either knee, don’t flex at the hip (leg coming froward), and don’t abduct your leg (lift out to the side) either. 

You can start standing with both feet on the ground and just try to lift one foot clear of the ground, following the above rules, by simply pressing the standing leg straight downwards into the ground. 

A good visual is to imagine your leg as a straight, tall, heavy telegraph pole, being driven into soft ground. No bending, no buckling. This movement will cause the non-weightbearing leg to lift clear of the ground. So the hips ‘list’ because the standing leg pushes down, not because the hanging leg raises itself up. 

The addition of balancing off a step is a progression from standing on one leg on the ground, which of course requires a little more balance and core stabilisation. So if you’re wobbling or not sure, lose the step and  just stand on one leg. The breathing... doesn’t matter, just breathe.