Within the Anglican Communion, indeed within the Church of England, there are a variety of understandings of the priesthood/presbyterate/ordained ministry and setting out an `Anglican understanding of the priesthood' is there fore difficult.
One thing which is, currently at least, the case is that (officially) it is only Bishops and Priests who can preside at / celebrate the Eucharist. Even this is under attack from some within the Communion, notably in the Diocese of Sydney who have put the question -- even to the some the imperative -- of Lay Presidency firmly into the spotlight.
One objection which I have heard to the practice of limiting Eucharist Presidency to ordained priests is that it sets priests up a s a class apart from the laity and implies that they are somehow `better Christians' and this is bad. I agree that clericalism can and has been a problem within Christianity and at times priests have almost discouraged congregations from being educated about their faith lest they become confused and have encouraged an infantile `Father knows best' mentality.
However, I do not believe that Lay Presidency is the answer to this problem. In fact, I think that in some ways, it buys into the same (flawed) model of ministry. That is to say, by focussing on the celebrant/president's role (and the fact that only priests can be celebrant/president), one is still downplaying the rôle of the laity. The liturgy is the work of the people and it is not just about what the person up front does, but about the corporate act in which all in the congregation are active participants. There are various specific tasks which are done in the course of the service but those who carry them out are not thereby more important than other members of the congregation.
I find this to be demonstrated by a High Mass: the priest presides; the deacon proclaims the gospel, intercedes and lays the table; the subdeacon reads the epistle and holds the book; the crucifer carries the cross; the acolytes assist with the preparation of the table, the ablutions and act as torchbearers (possibly with others); the thurifer and boat bearer look after the incense; and the MC keeps everyone in order; the choir leads the congregational singing and provides other music to the glory of God; members of the congregation read the OT lesson, bring up the the elements and offering; everyone participates in the words of the liturgy. The fact that different people fulfil these specific tasks week by week*, so someone might be crucifer one week and `just' sat in the congregation the following week, helps to remind us that we are all, whether we have a specific (individual) task or not, participants. I find it particularly powerful that occasionally one of the priests acts as subdeacon which is usually done by a lay person (albeit one with permission to administer the chalice) as this reminds us that the priest remains part of the laos although having a specific rôle within it.
This is an important thing to remember. By virtue of our baptism we are all called into God's service but that can take different forms one of which is the priesthood. This is not a sinecure or privileged position from which to lord it over the laos but it puts the priest into a specific relationship with the people.
If one considers the callings of Isaiah, Jeremiah and Ezekiel, the calling imposes responsibilities rather than giving them a position of privilege. It is not always a pleasant message which they are called to preach and it gets them into trouble at times, for example, Jeremiah ends up being thrown down a well for a few days.
In a similar way, priests stand in a certain relationship with(in) the laos. As the ordinal say they are to be `servant and shepherd', `messengers, watchmen and stewards'. It is not that they are necessarily `better Christians' (whatever that might mean) than a layperson but that they have been set aside to care for the flock. Presiding at the Eucharist is at the heart of this.
This is a priestly task; that is how it has been understood down the ages. By celebrating the Eucharist, the celebrant is put into that relationship, with its concomitant responsibilities. Lay presidency therefore seems to be a contradiction in terms. But why bother with ordination in that case? It seems to be that there is an interesting parallel with marriage here. St Paul implies that sex equals marriage.** This makes the idea of `sex before marriage' something of a contradiction in terms. however, the Church still encourages/expects people to get married first. That way the proper context is set up. There are vows made, responsibilities laid out and God's grace is invoked on the fallible human beings called to undertake this life.
Another objection which I have heard to the reserving of Eucharist Presidency to priests is based on the idea of the `Priesthood of all believers' and on Christ as High Priest. These are used to say Christian have no need of a separate class of `priests' within the Church and thus what is there to rule out `Lay' Presidency?
Firstly, the `Priesthood of all believers' is not in itself a scriptural phrase although the way it was quoted by evangelical friends made me think it was at one point.
Secondly, it is too often interpreted in a very individualistic way as though it means each believer is a priest rather than that we corporately are a royal priesthood. Yes, with Christ as High Priest and the veil in the Temple having been torn, we have direct, unmediated access to God but is this all our being a royal priesthood means? Or does it say something about our rôle/calling in relation to the rest of mankind: we stand to them as the Levites stood to Israel. this ten says nothing about structures within the Christian community. In order for all to grow and fulfil their callings in the world, we need to be nurtured in the faith and this is the rôle of the priesthood. They are a specific part of the body (the digestive system?) which enables the body as a whole to fulfil its tasks. Lay people are at the front line of mission whereas priests are more engaged in the behind the scenes support.
* Well, hopefully the choir is made up of the many of the same people each week
**1 Corinthians 6:16