To be a member of a local church is to take responsibility for a people and to have that people take responsibility for you. For someone to become a member of a church, they are saying that the church they belong to is a true church, rightly preaching the Gospel, walking out the Bible, and responding to the reality of Jesus in truth. Membership is a recognition and proclamation that we are united to each other and belong to each other in Jesus. The details of what we believe it means to be a member of a church is best spelled out by the Anchor Church member's covenant we make to each other.
For further reading see:
Church Membership by Jonathan Leeman
The Trellis and The Vine by Colin Marshall & Tony Payne