If I remember correctly, it was Fr. Aidan Kavanagh, OSB, in his book On Liturgical Theology, who observed that most of St. Thomas Aquinas' doctrine of the institution of the Church appears in the context of his discussion of the Sacraments. What is manifested here is an understanding of the Church as being a principally liturgical or sacramental institution. While subsequent developments in ecclesiology after Aquinas stressed the magisterial, juridical, and otherwise "pastoral" roles of the Church, as a teacher of doctrine and right discipline, the medieval stress exemplified by Aquinas is on the sacramental function. This is not to say that the other functions are unimportant: they are certainly important, and not even Aquinas' doctrine of the Sacraments would make sense without these other functions. Nonetheless, it is the sacramental character of the Church that really distinguishes her from her pre-Christian mode of existence in the Old Testament. Martin Mosebach points out (in chapter 3 of The Heresy of Formlessness) that doctrine and morals did not change when God became Man, in the person of Jesus Christ. What did change was the nature of sacramentality itself. In St. Thomas' teaching, following of course the Apostolic teaching of St. Paul, the fundamental difference between the sacraments of the Old and the New Laws is that while the former referred to Christ as future, as not yet come, the sacraments of the New Law refer to Christ, not merely as past, but also as present - that is, as being here among us now. The Old Law was the pre-figurement of Christ; the New Law is Christ Himself. If there is a reason to speak of the Church as Christ's "Mystical Body" it is this: the emphasis on His presence among us.
In the Gospels, just as much - if not more - as teaching, we witness Christ doing: working miracles, healing the sick, casting out demons, riding a donkey, purifying the temple, eating and drinking - but above all, suffering and dying and resurrecting. The Gospel is as much a catalog of the concrete and historical reality of Christ - I would say myth entering into history - as it is a catalog of his teaching and example. More primordially than being taught by Christ, or being given an example of how to act in our own lives (i.e. morally), we are simply being given the opportunity to see Christ, to touch Him, to encounter Him. This is why the apostles were saddened when He told them that He would be leaving them - first by dying, then by ascending to heaven. They knew that what He had given them, before and beyond His teaching and example, was first and foremost Himself in the flesh. When he promised them that He would still be with them after His ascension, until the end of time, working through the Holy Spirit, He was in effect providing them with the sacramental and liturgical assurance of their faith. He was assuring his disciples that they would not be deprived of the consolation of His real presence among them, though He was ascending to heaven. Accordingly, (and as another author, Laurence Paul Hemming, writes in Worship as Revelation) the meaning of the Ascension is thus to establish the reality and realism of liturgical signification itself: the actuality of His continuing presence in the sacraments of His institution, the Church. The fundamental role of the Church is precisely this continuation of His presence, even before the function of teacher and lawgiver. The crucial message of the Gospels is not primarily the doctrine and example of Christ, but simply the concrete and tangible presence of God to those of faith. The presence is not merely a tool for effective teaching, either speculative or moral, or a model of pastoral work; the presence itself is its own raison d'etre, a Good worthy to be contemplated for its own self-sufficient sweetness. This presence of Christ in the Church is the liturgy, especially the sacrament of the Eucharist. Or to say it again differently: the Church is the presence of Christ; the Church is liturgy; the Church is sacrament - not an "eighth sacrament," to anticipate a traditionalist objection; rather, the Church is her sacraments themselves. As Fr. Kavanagh would put it, the liturgy itself is how we do the Church.