To begin, I want to make it absolutely clear that the "important stuff" I mention in this post is what I've found to be, for me, the highlight points of the document, or in other words, the crucial points the document makes. Addressing the Triune God's activity in founding and sustaining the Church, while looking at the justifications for those claims, along with the relationship to the mystery of the Church to its people, and all the way to the "marks" needed to identify a church/ecclesial body will be addressed to further understand what we mean when Catholics refer to as their "Church".
For starters, God the Father, in His "utterly free and mysterious design of his wisdom and goodness, created the entire universe" (LG, 2), and He chose to raise up men and women to share in His own divine life. Despite man's fall through Adam, He never abandoned them, but at all times offered them the means of salvation (through Christ obviously). "Prefigured at the beginning of the world, this church was prepared in marvelous fashion in the history of the people of Israel and in the ancient alliance" (LG, 2). And it is in this Church which will be brought to glorious completion at the end of time.
Paragraph 2 of Lumen Gentium truly harps on the fact that God indeed prefigured this. One can't help but also look at the paragraph 1 of the Catechism of the Catholic Church and breath in the resemblance of the two...
"God, infinitely perfect and blessed in himself, in a plan of sheer goodness freely created man to make him share in his own blessed life. For this reason, at every time and in every place, God draws close to man. He calls man to seek him, to know him, to love him with all his strength. He calls together all men, scattered and divided by sin, into the unity of his family, the Church. To accomplish this, when the fullness of time had come, God sent his Son as Redeemer and Savior. In his Son and through him, he invites men to become, in the Holy Spirit, his adopted children and thus heirs of his blessed life" (CCC, 1).
Jesus now comes into the picture in Paragraph 3 of Lumen Gentium. The principle objective for Jesus is to carry out the will of the Father. As far as the Father is concerned, it was in Jesus Christ that it was most pleasing for Him to restore all things; and Jesus indeed did just that. It was the will of the Father that Christ inaugurate the kingdom of heaven on earth and reveal his mystery to us. Jesus preaches the Kingdom of God, and the Church ultimately declares the Kingdom of God has come about in Jesus' Life, Death, and Resurrection. Therefore, when Jesus decides to leave, the Church can continue preaching this utterly amazing truth.
Last but not least, the Holy Spirit is surely not left out of this shin-dig. The Holy Spirit has been given marching orders to see to it that this proclamation of Jesus (Life, Death, and Resurrection) is carried out strongly to the end of time.
Smack yeah, you read that right.
The Holy Spirit was also given a mission, that it can't bear (or is able) to be unsuccessful in, to allow Jesus' promulgation of his Father's Kingdom see the end of time. "By the power of the Gospel he rejuvenates the church, constantly renewing it and leading it to perfect union with its spouse. For the Spirit and the Bride both say to Jesus, the Lord, "Come!" (LG, 4).
Now that the declaration of God's masterminded plan has hit the record books, we can't ignore Christianity's many interpretations of what Jesus said and came to do. The universal church is seen to be "a people made one by the unity of the Father, the Son, and the Holy Spirit" (LG, 4). It is precisely this that drastically separates our (a Catholic's) theological thinking compared to one of our beloved Protestant brothers and sisters. For Catholics, the Holy Spirit came to vivify the Church, make it new, make it living. The Church is an act of the TRIUNE GOD, each one playing a desperately crucial part. On the other hand, for Protestants, they will conclude that the Church is only an act of Christ.
In order to address the justifications and sources for the claims that the Triune God sought to bring about the Church, and not just Christ, can be found in none other than Sacred Scripture (which has beautifully dispelled from Tradition). Scripture identifies the Church as many things. It uses symbols and metaphors to attempt to articulate for us what the Church is. Though not limited to just these interpretations, Lumen Gentium gathers from scripture that the Church is: a sheepfold, a flock, a farm, a field, a building, a holy temple, our mother, the spouse of Christ, and so on. Since this Living Word articulates the Church in this way, we must use Theology to help probe it's metaphors. Theology helps us understand how these images work well, but also how they don't (Just a small little Theo plug).
"The mystery of the holy church is already brought to light in the manner of its foundation" (LG, 5), meaning that since the Lord Jesus inaugurated his church by preaching the good news of the coming Kingdom of God, the Church has been equipped with one absolute mediator and "the way" of salvation. "For the Church is driven by the Holy Spirit to play its part in bringing to completion the plan of God, who has constituted Christ as the source of salvation for the whole world" (LG, 17).
Finally, the membership of the Church is determined by the mediation of the Sacraments, and in this unique Church of Christ, which we profess to be one, holy, catholic and apostolic, has firmly been rooted into history. It's foundation cannot be blemished. The Church will see to the end of time. The Church has always been one. The Church has always been the means of sanctification. The Church has always pleaded universality. And lastly, the Church has always and will always be prevalent in history.