I am of the generation that learnt Latin for 5 years in high school, and remember hours of conjugating verbs in a sing song fashion for Miss Walter, our classics teacher. One of those verbs was "spectare" (the Latin root of the word respect) meaning to watch, observe, look at, see, consider. These meanings have been carried across into the English word "respect" and when exercised in the context of relationships, foster a climate where one person looks to, observes and considers the other person's perspective. In doing this, we allow them to be individuals who have developed their own way of being in the world as a result of the genetic, social, cultural and God ordained influences that have shaped them.
Cloud and Townsend in "Boundaries in Marriage" include respect in their "10 Laws of Boundaries in Marriage", outlining how sticking to the Law of Respect fosters love by restraining self and allowing the other their freedom of choice. This means dying to self, not imposing my ideas on the other or wanting them to see things my way. Instead, by appreciating that they have their own way of understanding and viewing the world, and their own conclusions about how things should be, we give them permission to be themselves.
In practice what does this mean? Firstly I can listen to and respect the other person's view, even when I don't agree with them. A practical way to demonstrate that we are listening, hearing and respecting the other person's point of view is by using the skill of Reflective Listening. This can be accomplished by focusing purely on hearing and understanding the other when listening to them, not formulating our response to them in our head whilst listening. We communicate that we have heard what they are saying by giving a brief paraphrase of what they have said, opening with a phrase like "so you're saying..". Using this technique has the advantage of communicating to them that we have fully heard their point of view, and are respecting it by not immediately challenging them with our own perspective.
Furthermore, listening well in Christian fellowship is a gift we can give to others as Bonhoeffer highlights (Bonhoeffer 1954 p.97):
The first service one owes to others in the fellowship consists in listening to them. Just as love to God begins with listening to his word, so the beginning of love for the brethren is learning to listen to them.
Finally, respect generates safety for us to be ourselves since we are expecting the other to hear and value our view, even if they are not in agreement with us. Additionally, we are not expecting to be devalued, demeaned or criticised for being ourselves and stating how we see things. In her book "Couple Relationships", Elizabeth Tuetteman says "the heart of the matter in building a good relationship is as simple - AND AS DIFFICULT - as making it safe for your partner to be who they are as completely as it is possible to be."
Husbands, in the same way be considerate as you live with your wives, and treat your wives with respect...
1 Peter 3:7
...and the wife must respect her husband
Eph. 5:33