This is the top book I’d recommend to a lay person on church membership:

Jonathan Leeman. Church Membership: How the World Knows Who Represents Jesus. 9Marks. Wheaton: Crossway, 2012. 142 pp. 28-page sample PDF.

Some excerpts:

“Twelve Reasons Membership Matters” (pp. 79–81):

1. It’s biblical. Jesus established the local church and all the apostles did their ministry through it. The Christian life in the New Testament is church life. Christians today should expect and desire the same.
2. The church is its members. To be a church in the New Testament is to be one of its members (read through Acts). And you want to be part of the church because that’s who Jesus came to rescue and reconcile to himself.
3. It’s a prerequisite for the Lord’s Supper. The Lord’s Supper is a meal for the gathered church, that is, for members (see 1 Cor. 11:20–33). And you want to take the Lord’s Supper. It’s the team flag that makes the church team visible to the nations.
4. It’s how you officially represent Jesus. Membership is the church’s affirmation that you are a citizen of Christ’s kingdom and therefore a pasport-carrying Jesus representative before the nations. And you want your representation to be authorized. Closely related to this. . . .
5. It’s how you declare your highest allegiance. Your membership on the team, which becomes visible when you wave the flag of the Lord’s Supper, is a public testimony that your highest allegiance belongs to Jesus. Trials and persecution may come, but your only words are, “I am a Christian.”
6. It’s how you embody and experience biblical images. It’s within the accountability structures of the local church that Christians live and experience the interconnectivity of his body, the spiritual fullness of his temple, and the safety and intimacy and shared identity of his family.
7. It’s how you serve other Christians. Membership helps you to know which Christians on planet Earth you are specifically responsible to love, serve, warn, and encourage. It enables you to fulfill your biblical responsibilities to Christ’s body (for example, see Eph. 4:11–16, 25–32).
8. It’s how you follow Christian leaders. Membership helps you to know which Christian leaders on planet Earth you are called to obey and follow. Again, it allows you to fulfill your biblical responsibility to them (see Heb. 13:7, 17).
9. It helps Christian leaders lead. Membership lets Christian leaders know which Christians on planet Earth they will “give an account” for (Acts 20:28; 1 Pet. 5:2).
10. It enables church discipline. It gives you the biblically prescribed place to participate in the work of church discipline responsibly, wisely, and lovingly (1 Cor. 5).
11. It gives structure to your Christian life. It places an individual Christian’s claim to obey and follow Jesus into a real-life setting where authority is actually exercised over us (see John 14:15; 1 John 2:19; 4:20–21). It’s God’s discipling program.
12. It builds a witness and invites the nations. Membership puts the alternative rule of Christ on display for the watching universe (see Matt. 5:13; John 13:34–35; Eph. 3:10; 1 Pet. 2:9–12). The very boundaries, which are drawn around the membership of a church, yield a society of people that invites the nations to something better. It’s God’s evangelism program.

Related:

1. 22 Mistakes Pastors Make in Practicing Church Discipline
2. A Study of Church Membership and Church Discipline
3. A Popular Primer on the Church