The section on "The Unity of the Church" explores the first of the four "Marks of the Church": oneness (the other marks are holiness, catholicity, and apostolicity - say those three times fast).
Because in Christ the Church is one, it strives to be one.
Although this should be evident, the BOO makes clear that the Church as the Body of Christ cannot be separately related to the Christ, its head. The Body is one, the church is one.
To be one with Christ is to be joined with all those whom Christ calls into relationship with him. To be thus joined with one another is to become priests for one another, praying for the world and for one another and sharing the various gifts God has given to each Christian for the benefit of the whole community.
Echoing Paul's exposition of the Body of Christ, the BOO reminds us that we are knit together with those we may not otherwise want to be in relationship with. Christ calls all into a relationship, so we are called to serve one another as Christ serves us.
Division into different denominations obscures but does not destroy unity in Christ. The Presbyterian Church (U.S.A.), affirming its historical continuity with the whole Church of Jesus Christ, is committed to the reduction of that obscurity, and is willing to seek and to deepen communion with all other churches within the one, holy, catholic, and apostolic Church.
This is the meat of the section, in my opinion, for this is the question everyone is asking themselves. Especially in the PC(USA), where roughly every decade a group arises which threatens to split the numbers of our denomination, this is an important statement to make. We are not able to do anything to destroy the unity of the people whom God has called, but we do obscure it. When we separate, we make it harder to see the fact that Christ has called us all. Therefore, Presbyterians are called to reduce the obscurity. We have affirmed that we are the people who are committed to making it easier to see that Christ has called us all. We should not allow ourselves to consciously do anything which would communicate the opposite.
Implicit in this is the reality that we may profess with our lips that others are called to Christ, but we do not functionally believe it. We try to justify splitting ourselves off from others, but, truly, we have no ground to stand upon. As we try to make the case that we are having a "crisis of conscience" and are simply "looking for a place to stand" what we are really saying is that we do not trust Christ enough to be willing to stand next to others. It's not a "crisis of conscience" that plagues us, but a gag reflex at the thought that we are called to be priests for those other people. May God have mercy on our unbelief.