The man and woman share a name. Adam called the woman by his name. We have said before that names in Hebrew are important, and here it is an offering of an identity. Further, we note the leaving of parents. Everything is altered by the choice of this relationship initiated and brought about by God.
Marriage is a uniting of two people at every level.
The energy of sexual attraction brings about a oneness that is profound. The choice to marry means a commitment to one whole person for one whole lifetime. Reading of the wedding day of Adam and Eve reminds me of my own. I remember feeling fairly calm as I stood in front of the church with my friends and family surrounding me. I was not conscious of my emotions when the back door of the church opened and my wife and her father walked down the aisle, but I realized a moment later as we stood next to each other that I could not walk up the stairs to the platform.