Romans 12:4-5

For we have many members in our bodies, but not all members have the same function, 5 So we being many are one body in Christ, and individually members of one another.

I combined four and five, because I did not want to separate a sentence.
I like the comparison of the Church to a body, because of it's many applications, from the dependance of one Christian on the others, to the importance of unity. Here the meaning is greater if you view the verse in light of the previous verse. This explains why it is necessary that no one be conceited.
I also think that "individually members of one another," is a challenge for us to share life together, we need to do more than have the model church conversation: church goer 1: Hi, How are you?
church goer 2: Great and you?
1: Wonderful, see you next week.
2: Sure see you next week.
There's nothing wrong with the above conversation, except it does not go deep enough. How can you be a member of one another and not know each other?