This has been edited to include things learned from the comments.
The reason I'm a switch is because of what submission/domination mean to me in the context of a Christian marriage; most of it applies in other LTR contexts. But who knows what it means to others?
The submissive is giving their dignity, their trust, a measure of control over their body; they are accepting some humiliation and pain. They are saying "I will accept pain, I will abase myself, because I want to give you pleasure." My form of submission also pretty much always includes an element where the submissive is getting sexually excited with much less that the dominant has to offer; foot play is the major example of this for me. The submissive is saying "You are so wonderful, so beautiful, that only this little bit of what you have is enough for me". The submissive is expressing compliments and love through self-sacrifice; and that it is happy self-sacrifice is one of the greatest compliments. When I am the submissive, I feel good about giving, and thus about pain; I feel proud of humiliation. I enjoy it a lot within a marriage, but I would not enjoy it with someone I didn't love the way I would something simple and non-submissive.
The dominant has a much more psychologically passive role in my little world, even if it's more physically and mentally active. The dominant is receiving the compliments and the love and the trust. The dominant must dominate to allow the submissive expression. If the dominant is too hesitant, too mild, the submissive's feelings are not fully expressed. If the dominant goes too far, the trust is betrayed.
Missing from my analysis is any idea of why the pain and humiliation of the submissive is a good thing to me as a dominant. Certainly in an ordinary context it's bad. I'm all about giving her backrubs or my coat if it's cold. Why do I want it in a sexy context? I don't know.
In a Christian marriage the participants give rights over their bodies to each other; both the husband to the wife and the wife to the husband is specified in the Bible, not just one way. D/S play is the way I like to see that expressed; it's the fun way.
I figure domination and submission must mean very different things for people who are not switches, and likely in lots of cases for other switches too. What do they mean to you?