The Bible has 6 main metaphors it uses to describe the church. All of them are about relationships. Each of them sheds new light on a particular aspect of church relationships.
Bride - The church is the bride of Christ. The first and foremost relationship that exists in the life of the church is the one between Jesus and those who have experienced his love. This union is a sweet and mystical one, compared in Ephesians 5 to the union between a husband and a wife.
Body - The church is the body of Christ. This metaphor highlights the two dimensions of church relationships. First, it defines the church in vertical relationship to Christ. He is the head of the church, meaning that it can do nothing independent of him. What good is a body without its head? Second, it defines the church in the horizontal relationships of its members. Each and every member of the body is necessary and important (1 Corinthians 12).
Building - The church is the building of God. This metphor highlights the relationship that the church has with its past. It is built on the foundation layed by others (1 Corinthians 1-3, Ephesians 3). The church today cannot act independently of the church in the past. We are linked with our heritage. And it is throughout the last 2000 years of church history that God's presence and activity in the world is seen. The church continues to be built as his temple (Ephesians 2).
Branch - The church is the branch, connected to the vine of Christ. This metaphor highlights (similarly to the head-body connection) that the church is powerless to produce fruit unless it is connected to Jesus Christ through his word and prayer. This was Jesus' message in John 15.
Flock - The church is a flock of sheep. This metaphor defines the church's relationship to its leadership. We need our Chief Shepherd, Jesus Christ. And, we need the loving and caring shepherding ministry of pastors.
Family - The church is a family of brothers and sisters. This metaphor defines the church's unique identity. We have a special bond as the people of God that does not and cannot exist anywhere else. Just as a family lives and grows together, through good and bad, so too the church is a living and growing family of believers in Jesus Christ.