(1) The church is a Family
(2) With familial terms of Christ as the groom and the church as His Bride.
(3) The church is a Body, each with separate special functions and responsibilities, with Christ as its head, holding the entire body together and equipping every part to work as it should.
(4) The church is a New Temple [building], a Holy Priesthood, Branches of a vine, a Field of crops.
Corey Carey also brought up some good points that para-church organizations such as Campus Crusade for Christ, and InterVarsity, etc. are not church bodies in that they do not have the structure of a local body with elders and deacons. Larry added that they also do not partake of the sacraments of the Lord's Supper and Baptism.
I would go further to add that they are members of the universal or catholic church [not the Roman Catholic] but they do not stand in themselves as a local church body. The local church has many facets. Here are the 9 marks of what a church is according to Mark Dever [and I tend to agree with him].
(1) Expositional Preaching
(2) Biblical Theology
(3) Biblical Understanding of the Good News
(4) Biblical Understanding of Conversion
(5) Biblical Understanding of Evangelism
(6) Biblical Understanding of Membership
(7) Biblical Church Discipline
(8) Promotion of Christian Discipleship and Growth
(9) Biblical Understanding of Leadership
I also think that the church should have relationship between people from birth to very elderly. They must be in a community that they can share Christ in. They must have many professions and gifts to serve the body and live and speak the gospel to others.