A membership covenant is simply an articulated summary of the agreement between church members. Historically, membership covenants were quite common among Protestant churches, including Baptists, Methodists, Presbyterians, and Anglicans. And many churches still use them today.
As a matter of fact, all local churches have some kind of membership covenant, even those churches that don't have a formal status of "church member." Written or unwritten, formal or informal, there is always some sort of basic agreement made between those gathered in the name of Christ for public worship and edification.
That agreement may be so thin that it is basically an agreement to be present at the same time in the same building, but agreement is the essence of unity among those who gather together as a church.
Gathering in agreement and in the name of the Lord Jesus Christ is fundamental to the definition of what it means to be a Christian church.
That said, many churches publish a formal membership covenant. The purposes behind such a thing are manifold, but a simple and straightforward reason to have a formal membership covenant is so that individual members will know what is expected of them and what they should expect of one another.
One can read the whole New Testament, searching for every "one another" command, and thus summarize the biblical obligations and privileges of church membership, but it sure is easier and clearer if we can all agree on a basic set of promises that aim at representing a faithful summary of such things.
Membership covenants of various lengths and content have been published over the years, but I am particularly fond of one authored by J. Newton Brown. Brown's covenant was published by the Baptist Sunday School Board (now LifeWay) in 1853, and it was printed within the 1956 Baptist Hymnal because of how widely it was being used among Baptist Churches in America.
As with all membership covenants, one has to decide what to include and what to exclude. Truth be told, I think at certain points Brown's covenant seeks to bind the conscience in ways that the Scripture does not, so I do not endorse it entirely. But many features make it commendable.
As early as November of 1940 (though probably earlier), when First Baptist Church of Diana, TX (the church I pastor), was still called James Baptist Church, Brown's membership covenant was formally embraced as the standing summary of members' obligations and privileges.
The words below are a duplicate of that old Southern Baptist covenant (odd spelling included), which was adopted by those early members of FBC Diana.
Having been led, as we believe, by the Spirit of God to receive the Lord Jesus Christ as our Saviour, and on profession of our faith, having been baptized in the name of the Father, and of the Son, and of the Holy Ghost, we do now in the presence of God, angels, and this assembly, most solemnly and joyfully enter into covenant with one another as one body in Christ.
We engage therefore, by the aid of the Holy Spirit, to walk together in Christian love; to strive for the advancement of this Church in knowledge, holiness, and comfort; to promote its prosperity and spirituality; to sustain its worship, ordinances, discipline and doctrines; to contribute cheerfully and regularly to the support of the ministry, the expenses of the Church, and the relief of the poor, and the spread of the Gospel through all nations.
We also engage to maintain family and secret devotions; to religiously educate our children; to seek the salvation of our kindred and acquaintances; to walk circumspectly in the world; to be just in our dealings, faithful in our engagements, and exemplary in our deportment; to avoid all tattling, back-biting, and excessive anger; to abstain from the sale and use of intoxicating drinks as a beverage, and to be zealous in our efforts to advance the kingdom of our Saviour.
We further engage to watch over one another in brotherly love; to remember each other in prayer; to aid each other in sickness and distress; to cultivate Christian sympathy in feeling and courtesy of speech; to be slow to take offense, but always ready for reconciliation, and mindful of the rules of our Saviour to secure it without delay.
We moreover engage that when we remove from this place we will, as soon as possible, unite with some other church, where we can carry out the spirit of this covenant and the principles of God’s Word.
Whether your church has a formal membership covenant or not, it is the privilege and obligation of every Christian to seek out intentional, meaningful, and regulated relationships with other Christians.
May God bless your efforts to love Christ and to love His people by giving yourself to such relationships within a local church nearby.