Why do we do what we do, there are many things in a D/s relationship that seem strange to people who do not understand what that relationship means. There are many different variation to D/s relationship, for different folks it has a different meaning. It all comes down to two people (adults) giving them permission to explore their desires and it does not matter what it is as long as it between two consenting adults. When a submissive a collar in public and her or his Master or Mistress walks in front of them and the submissive follows behind them, most people in society will not understand they dynamics of the relationship between the two or more adults unless they have experience in that type of a relationship.
I believe that in D/s the submissive is a desire, a need and a want to achieve a certain level of comfort within themselves as well with whoever they belong to. To have a purpose of belonging is a greater desire and also great pleasure in receiving a sense of being owned and protected by someone.