He first compared the three parts of the Trinity to the three states of matter that naturally exist in our day-to-day lives: solid, liquid, and gas. Any element can move through these phases, taking on unique properties in each form, yet still be the same element the entire time. That alone stands as a good analogy, but he took it a step farther and made the comparison within our bodies.
God the Father was represented by the solid form of the skin, the organ that encases us. I would take that a step farther and say that all of our tissue and bone are representative of the Father. It is through Him that all of our reality is shaped. Any experiences we have with our world or one another only exist due to His creation, just our skeletal, muscular, and tissue structure define what we can do an experience in life.
Our blood--a liquid--represented God the Son. It is the Son's sacrifice, in blood, that redeems us, that reaches to every tissue in our body and animates us. He is always a part of us, healing us, and allowing each cell within us a chance to stay alive.
Finally, the our breath--a gas--represented God the Holy Spirit. The Spirit energizes us, fills us with power, and allows us to communicate with one another. The Spirit not only comes into us, but we have the means to pass the Holy Spirit on to others as well.
In all, we are one body, working together with these various forms of matter. So to is God, in whose image we were created, all three Persons of the Trinity, yet still one God that works to make our lives, our world, our universe a better place. We might experience each of Person of the Holy Trinity in different ways, but together they are our one Lord.