In the Incarnation, Christ took up our humanity. He then bore that humanity to the Cross, and rose again by the promise of the Father. While human, He spoke- He was- the definitive Word of the Father. In His presence at the Wedding at Cana, Christ elevated marriage to the state of a sacrament of the New Covenant. It was already a primordial sacrament in the sense that it imaged God's love for His people. It was already a powerful symbol; but now Christ brings it to be sacramental in a new way. The meaning of marriage is disclosed in Christ. Just as He shows us what the human being is, Christ's relationship with the Church shows what marriage is.
Marriage is a created reality. It was instituted by God and it is part of His divine plan of salvation. Speaking of marriage as a "purely natural institution"- of society, of whatever- is not real. It does not see what it is. The union of man and woman is related to what God wants His relationship to the human being to be.
The Fathers of the Church looked at marriage as a state of life, in comparison with virginity. They saw it as a way to follow Christ- though perhaps not always in the fulness of the way we understand that today.
When the world was Catholic, the Church took that time to define what is specific to the seven sacraments. Think the classic definition here of "visible sign instituted by Christ to give grace."
As the Protestants began to challenge, well, everything, the Church's understanding of marriage tended to veer away from the state of life to the contract. Luther and Calvin say that marriage is only a contract and part of the natural world. The Church says, no no, the contract is the sacrament (especially evident through Leo XIII in Arcanum, 1880). The Church kind of adapted to the framework in which the questions were being asked: the utter depravity of nature, human nature being irredeemably sinful and only covered over by grace (i.e. dung hill covered by snow). One of the things lost in Protestantism- perhaps the thing lost- is the sacramentality of the world and creation.
So we're trying to recuperate this understanding. You can see this movement in the documents of Vatican II and of course our beloved Pope (St.) John Paul II. The Church approaches the sacraments in light of Christology, ecclesiology, and anthropology. Christiam spouses "signify and partake of the mystery of that unity and fruitful love which exists between Christ and His Church"(Lumen Gentium 11).
Read Gaudium et Spes 48:
Authentic married love is caught up into divine love and is governed and enriched by Christ's redeeming power and the saving activity of the Church, so that this love may lead the spouses to God with powerful effect and may aid and strengthen them in sublime office of being a father or a mother.(6) For this reason Christian spouses have a special sacrament by which they are fortified and receive a kind of consecration in the duties and dignity of their state.(7) By virtue of this sacrament, as spouses fulfil their conjugal and family obligation, they are penetrated with the spirit of Christ, which suffuses their whole lives with faith, hope and charity. Thus they increasingly advance the perfection of their own personalities, as well as their mutual sanctification, and hence contribute jointly to the glory of God.
The sacraments are the introduction of human life into divine life. Man is introduced into the Body of Christ at Baptism. His participation into the sacrament that Christ is (of the Father) is physical (head and body), nuptial (Eph. 5, Church as bride) and universal. Sacraments have to do with your relationship with Christ, which in turn is the relationship with a God who is Triune. Your whole life is called to be introduced into divine life, eternal life, which is the life of a God who is a Being-with. Being a person is to be-for God, others. The spousal gift of self must be seen in this light and in this understanding of what it means to be a person. Human love must enter into the logic of the gift.
The unity of the two in marriage is secured by the Holy Spirit. Cardinal Ouellet of Quebec wrote a beautiful article in which he wrote, "The Holy Spirit grants to the spouses a participation in His mode of being a communion of persons." Something like that. WHOA people. That's a huge deal! Because the Holy Spirit is Love, charity itself. He is what the Father and the Son are together, He is their communion, their bond of love. He is called distinctly what they are in common. The life of God is given to us in the Holy Spirit.
Marriage is also a historical reality. It is an event within history- this man and this woman join their lives together until death. It requires freedom and man's participation. Sacraments aren't like vending machines- the God who created you without you will not save you without you. (Augustine) The grace to participate in Christ's life is the same for all couples; but holiness makes a difference. The capacity of the container determines how much one can be filled!
Finally, marriage always has an ecclesiological character; it is always in and through the Church that grace passes. In this we recall the Marian dimension of the Church as Bride and Mother. Also the communion that the Church is; the unity of its members. The Church recommends that marriage be celebrated in the context of the Eucharist because it is integral to the nature of love itself. "This is my body, given for you." We are called to see how deep marriage gets into the structure of reality; a reality created by a God who is Love.
I think that's all the studying I'm doing for that question!