"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 the one body -- whether Jews or Greeks, slave or free -- and we were all given the one Spirit to drink.... (I Cor. 12:4-6, 12-13 NIV)
This classic passage of Paul's in I Corinthans lays out in careful detail the doctrine of the unity and diversity of the Church, described as Christ's body alive on the earth. He makes an analogy to the physical body, which has many parts but functions as a unit. The description is sufficient to make the relationship clear in practical life.
Notice that both principles, unity and diversity, are equally ultimate. There is therefore in Christianity no aspiration for "pure" unity, which is Eastern monism, nor "pure" diversity, which reduces to relativism and chaos. Instead, both principles balance each other in a stable structure of "organic unity" such as we see in the human body or any other living creature.