Davinci said that the nose forms the face's character. So, then what are people saying with their nose rings? Sometimes, it's a cultural statement. There are some African tribes have a nose ring given to a bride. (Yes, size is relative...) Other cultures believe that piercing specific areas of the nose will ease the pain of menstruation and childbirth. Where I live, in America, nose rings are mostly symbols of expression and rebellion. Often both.
We are born with our faces looking the way that they do. None of us are given any sort of choice. So many want to change that image in the mirror. Want to let their inner selves shine. By having a nose ring, or any sort of body modification, we can directly influence that first moment, that first impression. We have control how others see us.
To not just be defined by what nature, or possibly illness and/or injury, has given us but by what design we choose is a freedom. The joy to just exist, as you want, appear as you want, be what you want. Even the choice to not add a modification is an expression. Again, no need to change if you don't want to. Our character is what we make of it and how we choose to show it is up to us.