Let me see if I can help you with the first part of your question.
There are many parts to this dynamic, and it is up to each couple what best suits their needs.
For me? My little girl has placed herself in my hands. No walls...no defenses...open and vulnerable. She gives me every part of who she is no matter how shameful, or embarrassing it might feel to her. She submits willingly and freely to my desires and wishes. She moves between the coloring, giggling, sometimes bratty, pigtailed, innocent and adored little girl sitting in daddy's lap, and the adult woman I love, as her needs require.
Why? More importantly how?
She knows that there is nothing she could say, or do that will turn me away. My acceptance is absolute. Her entire world is in my hands, and I take the responsibility very seriously. It's sometimes difficult to hand down discipline. This is the love of my life, but she expects it, and I do my best to be firm but fair. When we play it is with a freedom so profound it just can't be put to words. No fear. That's the best I can do. The trust she has granted me is one of the most humbling experiences I have ever known.
With all that how could I be anything less than her daddy?
I don't really know much about the MD/lb dynamic. I would imagine it isn't the same just as there is a large difference between a Master and a Mistress.
I hope that helps