What about mission?
In love, God created the cosmos as a time/place in which to share his triune love and life with his creation. And because his love never ceases or diminishes, he became Redeemer to rescue his creation from its inability, due to the fall, to live in communion with him. As Creator and Redeemer, God has, from before time, been on mission.
The mission of God (missio Dei) in creation and redemption originates in the heart of the Father (John 3:16-17), and is accomplished through the Son of God, in the power of the Holy Spirit. In redemption, the Father sends the Son, who through his incarnation, life, death, resurrection and ascension, and sending of the Holy Spirit, reconciles all humanity to the Father. In this great missional act, the Father is the sender, Jesus is the sent one (the missionary) and the Spirit is the sending agent. And note that this mission is not finished. It continues with Jesus' ongoing intercession on our behalf through the power and indwelling of the Holy Spirit (Heb 7:24-25).
It is here that the church comes in. Jesus sends the Holy Spirit to form, call and gift the church to share in his ongoing ministry, which is fulfilling the Father's mission to the world. In short, the church exists because of, and for God's mission. The church is no mere 'tool' in God's hand, but is called to actively participate (partner as co-workers) in mission with him.
Mission = discipleship
Since the ascension and Pentecost, what God is now doing in the world in and through the church has principally to do with discipleship. This aspect of God's mission is not about 'getting people saved' (God has accomplished that already in Jesus), but about getting people into their salvation - helping them be (live) saved. This missional work (ministry) is about illumination, education and application. Jesus is working in people's lives in all three areas through the Holy Spirit. The church is called to participate by bearing witness to Jesus (Acts 1:8). It does so by sharing in Jesus' ongoing acts of healing, mercy and forgiveness; and by proclaiming with Jesus the stunning truth of the gospel (a declaration that includes inviting and empowering people to follow Jesus as one of his disciples).
In solidarity with the world
According to Karl Barth, the church participates in this ministry by living in solidarity with the world. Doing so means sharing with Jesus as he shares the world's suffering (due to sin), and its hope, which is grounded in the "free grace of God" in the person of Jesus (see Church Dogmatics;IV/3, p773, quoted by William Pannell in Evangelism: Solidarity and Reconciliation,Incarnational Ministry, p197).
Through incarnational ministry
According to Barth, the church finds its reason for being not in itself, but in this incarnational ministry with Jesus. God, in Christ, exists for the world - his supreme act of love is the incarnation by which he came to the world, becoming part of the created order, while remaining its Creator and Sustainer. In so doing, he reconciles the creation back to God. And his church, his "body" on earth (1Cor 12:27), is called to share this ministry with Jesus. Note, however, a word of caution: Our calling is to incarnational solidarity with the world, not conformity to it. As Barth notes, the church cannot say "yes" to the world, if it cannot also say "no." Here is the genius of Jesus himself - a friend of sinners, yet without sin of his own.
Reconciliation = incarnation
Pannell notes that the church's inability to stand in solidarity with the world is largely due to a lack of understanding that reconciliation is a function of incarnation. The reconciliation of the world to God is accomplished not only at the cross, but in the entirety of the incarnation. Thus reconciliation, because it is in the incarnate Son of God, is both personal and permanent. Jesus remains forever human on our behalf.
And now Jesus is making himself known - making this reconciliation that all people have with God in him, an experienced, personal reality (2Cor 5:20). Jesus is doing this ministry principally through his human presence in the world, in and through his body, the church, sent to stand in solidarity with the world - sharing its plight and proclaiming and demonstrating to humankind its one and sure hope.
And so we return to our original questions: Why should the church be concerned about mission? And what does mission look like? In both instances, answers are found in the person and work of Jesus - the Son of God incarnate, who stands in solidarity with the world. Let us be among his disciples - those who not only hear his voice, but actively join with him as he, in the power of the Spirit, helps people live into the reconciliation with God that they have forever in and with him.