I often hear it said that if you join a local church, you haven't just joined a branch of the church, or a part of the church. You are a member of the church. Each local church is the church. At the same time, the church throughout the world is one.
One thought just struck me that makes this clearer.
In the book of Exodus, the people are told how to build a tabernacle, a tent in which God can live. One of the pieces of furniture in that tabernacle is a golden lampstand. It symbolises that God lives amongst his people.