Sharon Rees
Calvin starts off this section of the Institutes by answering the question - why do we need the church anyway? "God, therefore, in his wonderful providence accommodating himself to our capacity, has prescribed a way for us, though still far off, to draw near to him." (4.1.1) The church is the way we get closer to God, and care for the body of Christ entrusted to us. Furthermore, the church is a mother - nurturing (4.1.2), a teacher - preaching the Word of God (4.1.3), and a gardener - planting and watering for God who gives the growth (1 Cor 3:7). Toward the end of this section, Calvin admits that the church is never perfect, but why would we forsake a mixture of good and evil for total imperfection?
What is the distinction between the invisible and the visible church? The invisible church, according to Calvin, are those already elected into God's presence (4.1.7). Members of the invisible church are dead, living, and arguably, not yet among us. We worship with the visible church each Lord's Day. The catch is that God knows the difference and we don't. So instead of trying to separate the sheep from the wolves ourselves, we should take care of everyone in front of us so that we might not accidentally harm the sheep (4.1.8). (Calvin does allow later for some corporate sorting [4.1.15], but that shouldn't destroy the main principle.)