Let's start with a basic picture of human society, which I think is at least approximately true. Human beings are both sympathetic and rational, and for both reasons tend to combine their efforts in with others. In some of these interactions, the people involved are interacting in order to have some good that they have in common with others through the interaction. This common good is literally common; it is not a distributed good, divided among the people interacting, and it is not a collective good, distinct from the good of each. It is a good held in common, each individual's good and yet not divided among them. Systems of such interactions are called 'communities' after this good shared in common. In rational interactions with common good, we have rational principles governing how the common good is to be handled in the interactions; these are obligations and norms. When a community has in itself all that is required for the common good it has as a community, it is a complete society. The explicit obligations and norms of a complete society, when made explicit by the actions of all of the members of the community, or made explicit by those whom the members of the community treat as having the relevant authority, are called laws.
Let's also consider the nature of the Church, with an account of its origin that I am greatly simplifying but that I think is also at least approximately true. The Church by its nature does not arise out of a set of responses of its individual members; it is not the Jesus fandom. It is an institution, in the very literal sense that it was instituted by Christ and the early disciples operating on behalf of Christ. Even in the life of Christ it had rites and structured practices (baptism, preaching, healing missions) formed under his direction. It likewise had roles that were at least semi-formal and had some specific responsibilities -- the book of Acts lists the roles of authority in the Church as the Eleven (i.e., the Twelve Apostles minus Judas), the Brothers of the Lord, the Women, and Mary the Mother of the Lord. The last of course is a sui generis role; the Apostles seem to have been the primary authority, with the Brothers of the Lord primarily concerned with the role of Christians in Temple worship and the Women primarily concerned with administering the material needs of the Church, although our knowledge of the role of the latter two is very hazy and limited, because only the Apostles had a role that made it possible for them to provide a stable organization for the Church as a whole, and because the Brothers of the Lord did not survive much beyond the destruction of the Temple and the Women, whose original unity seems to have been that they had been wealthy women personally healed or exorcised by Jesus who were returning the favor by providing money and other help to Jesus and his disciples, seem to have broken up into various diverse practices and traditions. The Apostles in organizing the Church established what seems to have been a fairly wide variety of different roles, of which the role of Supervisor (or 'bishop', to use the English modification of the Greek word for 'supervisor') was particularly important. The very early Church, however, seems to have been quite flexible in terms of the offices used, and one reason the role of Supervisor became dominant is that it literally involved the Apostles delegating some of their own supervisory functions, which could be said of no other role. The Church is organized under a particular commission, part of its very institutional structure: to go into all the world, baptizing and making disciples; it thus has both a sacramental and doctrinal aspect to it.
Therefore the Church is a community to which you are called, into which you are initiatiated, and within which you are part of an organization. Many of these features are not made by those who are members but received by them as part of the process of tradition, vocation, initiation, and participation. The Church pre-exists any of its members and is received by its members as involving common good that is higher than any human good, and part of that common good is the community itself. The Church itself is also a complete society, since it has everything in itself that its common good requires.
So far, so good; I am simplifiying, but this is in its broad outlines a fairly standard kind of ecclesiology. However, I think there is another aspect that gets forgotten. The Church as outlined above is a received society rather than a formed society; that is, its members receive the common good that makes it a community, including its sacramental and doctrinal hierarchy, whose existence depends on its institution from Christ and the Apostles rather than the members themselves. But when human beings have a common good, they form communities, and therefore the members of the Church, sharing the common good they receive from divine institution, form a society that depends on its members. This aspect of the Church I call the 'liturgical commonwealth'. It forms within the Church as part of the Church, and includes all of the members of the Church. The Church is not reducible to the liturgical commonwealth (because it is not reducible to the kind of society it is insofar as it depends on its members), but the Church is the liturgical commonwealth.
The common good of the liturgical commonwealth includes all of the doctrine and the sacraments of the Church, and thus all of the hierarchy which supervises the doctrine and the sacraments. However, as with every other complete society, the liturgical commonwealth as such has authority over itself to protect that common good, and this is a power that belongs to the whole people who are part of it. Bishops have supervisory power over doctrine and sacraments, including the power of canon and liturgical law, but the whole community can by custom and various means of organization establish norms and even laws that are distinct from this.
This adds a layer of complication to ecclesiology -- the Church has to be considered both insofar as it is a received hierarchy and insofar as it is formed by its members -- but it also, I think, explains a great many things. There are many powers bishops and priests have historically had that are not strictly required by their doctrinal and sacramental mission; they are powers that have been given by the communities they served, because the community needed certain functions to be fulfilled and it was more convenient to attach it to the already-received episcopal or priestly office than to invent a new office. Likewise, there have been many roles that are distinct from the received hierarchy that have nonetheless played an important role in the Church. Monks and nuns and the like are an obvious case; they are now more or less formally integrated into what we usually think of as the received hierarchy, but this is actually a relatively new thing, something that took many centuries. All of these positions are things that were not necessarily done as an extension of episcopal organization, and yet developed a considerable amount of authority and influence just by the custom of the people. That is, the roles were generally created by the people as part of their way of upholding the common good, and then the bishops, exercising their supervisory power, organized those roles that the people had developed. (There are particular kinds of monastic that were invented by bishops, but in those cases the bishops were generally using a pre-existing role, developed by the people, as a model that they then adapted.) Other roles that have certainly been important for the Church but which were formed by the people rather than received as part of the instituted common good, are Christian kingship and Christian knighthood. Recognizing that the Church is a liturgical commonwealth clarifies the functions of such roles within the whole order of the Church.
In English we often call the hierarchy-constituting sacrament, 'holy orders'. But the original name for it was just Order. And the 'order' in the sacrament of Order was not a specialized term. Every society whatsoever has order, in the same general sense that 'order' was applied to the sacrament of Order; every society has to ordain (i.e., set in order) things for its common good. The Church has an instituted sacramental order, but as a liturgical commonwealth, it also has the same general sort of social order that human societies tend to have. And just as we have 'holy orders', that is, sacramental components of the sacramental order, we also have what might be called 'social orders', that is, social components of the social order. They are not equal, because the sacramental order is itself part of the common good that the social order is formed to protect and preserve, and because the supervisory powers of bishops are conferred sacramentally but are both sacramental and social in scope. (Christian marriage, like the clergy, also exists in both orders, and plays an important role in structuring the liturgical commonwealth.) But they are distinguishable. We can see this even in the clergy; the clergy are primarily structured by the sacramental orders (deacon, priest, bishop), but there are clearly distinctions among clergy that are social-order distinctions (monsignor, cardinal). But there are social orders in the Church that we primarily associate with the laity as well; again, Christian kings and Christian knights are an example. Some, like Christian kings and Christian knights, have been explicitly given a kind of sacramental recognition for their role in upholding the common good of the Church; that is to say, there are sacramentalia (sacramentals) associated with them, in the form of various blessings and Christian rites that at various times and places the Church has recognized. But the lay social orders themselves develop as part of the laity just living their lives in the Church, not because of these sacramental recognitions. Thus recognizing that the Church is also a liturgical commonwealth can serve to clarify the role of the laity in the Church, since the laity often participate in the actual work of the Church through social orders and roles that could, if necessary, be formalized as social orders, and because the laity play a major role in shaping the customs and norms of the liturgical commonwealth.
The idea is that the Church is therefore a kind of double society, the society into which we are called and which we form in light of the society into which we are called. Thinking in this way
(1) provides a way of clarifying a number of ecclesiological questions, like cultural and local powers of clergy, like the role of the laity in the Church, like the way in which the Church is both a divine and a human society, etc.;
(2) gives an ecclesiology that recognizes the priority of the sacramental and doctrinal order without reducing the Church to that;
(3) gives an ecclesiology that is flexible enough to account for the real importance of the customs of the people and Christian culture without reducing the Church to that.