The way I understand it, (or misunderstand it), is that we are all God's kids. That is whether we believe it or not, or whether we want it or not, you cannot change that fact. All of us make up the one son. We are members in the body of Christ much as the arm is a member of the human body. That is why it is said that I literally cannot hurt you, without hurting myself because there is no seperation. Einstein said that the grand illusion is that there is more than one of us here. The Upanishads believe that enlightenment comes when we conclude this, and Jesus emphaitically taught this. To sum it up, unity means when I look at you I see me. When I am downtown my car swings by the mission, and I see all of Gods kids waiting for a bowl of soup, I see that they are me, and I am them. No seperation Ian. We have to come to a place where ther is no seperation, then we are one in Christ.
The Bible says "The body is a unit, though it is made up of many parts; and though all its parts are many, they form one body. So it is with Christ. For we were all baptized by one Spirit into one body—whether Jews or Greeks, slave or free—and we were all given the one Spirit to drink." This means Christians believe that God created everyone equally and we are brought together by God's creation - ourselves. He "must us in his image" and therefore we are all the same. This is what I have observed as a non-Christian, but if you wanted a more accurate definition a Christian would probably have a better answer.
Supporting/praying for one another in good/bad/struggling times - assisting one another in keeping their 'eyes on the prize' - focused on doing God's will as individuals and the church collectively.