Let’s answer the purpose of the Church by first recognizing what the Church is and how the Church may be recognized. Ascertaining the what and how of the Church greatly factor into the very purpose of the Church, that is, they essentially answer the question why the Church?
Let’s start with a distinction. Our use of the capitalized word “Church” denotes the “one, holy, catholic, and apostolic Church,” as opposed to one’s congregation — a “church.” So “Church” denotes the big picture, while “church” demarcates your localized participation in the Church. Additionally, the Church present on Earth should be understood as contiguous with those Christians who have died in Christ and whose spirits are with the Lord while their bodies await the resurrection. In other words, although the Church is one, yet it is not entirely manifest as such in the here and now. Still, the dead in Christ are of the Church every bit as much as we who abide in this life.
Now, what is the Church as we experience it in this mortal life? Simply put, the Church is Christ manifesting his body through “the assembly of all believers among whom the gospel is preached in its purity, and the holy sacraments are administered according to the gospel” (AC VII:1). This might be a surprise to some: The Church has a Christ-centered reference, not a human-centered reference. It is less about the activity of people (assembling and calling themselves a “church”) and everything to do with Christ’s activities and presence. We neither engender the Church nor self-designate it. We don’t make Church happen. Only Christ can do so. Consequently, the Church is the creation of Christ by the word of the gospel: “through the gospel alone the Church is conceived, formed, nourished, generated, instructed, fed, clothed, adorned, strengthened, armed and preserved—in short, the whole life and substance of the Church is in the Word of God,” wrote Martin Luther (WA: 7:721). Thus, the Church proceeds from not merely Christ’s victory on Golgotha, resurrection from the tomb and ascension, but from his very being. The Church, then, is the result of divine activity within “the assembly of all believers” in which the Son is given in the power of the Holy Spirit as “the gospel is preached in its purity and the sacraments are administered according to the gospel.” In this way, the Church is purposed by Christ to be the ark of salvation.
Ascertaining the what and how of the Church greatly factor into the very purpose of the Church, that is, they essentially answer the question why the Church?
Such an orientation advances our understanding of the Church as Christ’s self-giving through the word and Sacraments as the means of grace and the very means by which God the Father, Son, and Holy Spirit articulate and manifest the Church as God’s kingdom in this world. The Church, then, is “how” and “where” God’s gracious will is “done on Earth as it is in heaven” (Matt 6:10). Herein we find the chief purpose of the Church: The Church exists so that the Father would establish, further, preserve and glorify his kingdom on Earth through the reign of the Son within his kingdom people by the power of the Holy Spirit. The Church exists, then, as the domain or kingdom of the Triune God’s self-giving in love, mercy, grace, truth and peace. The Church is the what, how, where and why of the Holy Trinity’s self-giving for our salvation and sanctification.
Here we find yet another purpose of the Church emerging: To vouchsafe the gospel-boundaried commissioning of water, bread, wine, and duly called and ordained clergy keep the object of faith—Christ—and his word always at center and as the proper object of worship and adoration. When the Church is faithful in the stewardship of her Bridegroom’s gifts, then the Church does the world a great service in facilitating the reality of God in Christ with us and for us. Another way of saying this is that the purpose of the Church is to direct faith to where and how Christ is present. And so, the purpose of the Church is to demarcate boundaries, establish limitations, and underscore specifications according to the Scriptures as to what constitutes God’s kingdom and what does not (1 Tim. 3:15).
Where, therefore, the holy gospel is preached, and where baptism is administered, along with absolution and Holy Communion, in accordance with the Scriptures there is true faith, and where true faith exists so does the one, holy, catholic and apostolic Church.  By the gospel of Christ, the Holy Spirit elicits faith, begets the Church, and constitutes her authority and raison d’être: “The sure mark by which the Christian congregation can be recognized,” writes Luther, “is that the pure gospel is preached there. For just as the banner of an army is the sure sign that they have taken the field, so, too, the gospel is the sure sign by which one knows where Christ and his army are encamped” (LW 38:305).
The Church is the what, how, where and why of the Holy Trinity’s self-giving for our salvation and sanctification.
The gospel and the Sacraments are “in” the assembly of believers as the service which is entrusted to the assembly of believers and which is performed by it.  But exactly how the Church is present in this world is part of the generosity of the moment: it cannot be explained; it is a mystery: the work of the Holy Spirit, and so an article of Christian faith. We believe it to be so because the word of God says so. To say anything otherwise would nullify it as an article of faith and instead make it something of this world and entirely subject to human powers.
Other purposes of the Church that could be considered (e.g., raising up ministers or exercising discipline or even Jonathan Edwards’ assertion that the purpose of the Church was for the Father to provide a bride for his Son). We close, however, with this thought, namely that the purpose of the Church is to train you—the baptized—to be at home in God’s kingdom right now in anticipation for the time when God’s kingdom will be manifest in all its perfections on the Last Day. Rephrased, the purpose of the Church is to normalize living like resurrection people with God in our midst in the here and now for when the day of resurrection comes. Think, therefore, of yourself on a journey home (when heaven is finally and fully on Earth), only to find out that when you arrive, everything is strangely and comfortably familiar because the extraordinariness of heaven-on-earth has been the ordinary business of life in the Church in the here and now. The Church acclimates us amid time for eternity by garnering within us a deep and even necessary recognition and appreciation for God’s love, wonderment, goodness, truth, and beauty in the ordinary-extraordinary things we experience in the assembly of believers.