An Apostolic Constitution is an instrument which the Holy Father has used for the erection of new dioceses. See some examples here. Apostolic Constitutions have also been used for the restructuring of the Roman Curia, the promulgation of the Code of Canon Law, etc. In other words, they are a very significant means of establishing something new.
The forthcoming Apostolic Constitution enables the establishment of Personal Ordinariates which will allow former Anglicans to enter full communion with the Catholic Church while preserving elements of the distinctive Anglican spiritual and liturgical patrimony.
A Personal Ordinariate is not a Personal Prelature, which is already foreseen in the Code of Canon Law (Cann. 294 - 297) Personal Prelatures consist of presbyters and deacons to promote a suitable distribution of presbyters or to accomplish particular pastoral or missionary works. Lay people are not, properly speaking, members of personal prelatures [UPDATE: see clarification in the combox] but they can dedicate themselves to the apostolic works of the prelature by agreements entered into with the prelature in accordance with the prelature's statutes.
An Ordinariate of this nature I think has a temporary nature, which could develop in either direction. It could either become redundant, in which case the clergy and laity would become subject to the bishop of the diocese in which they have domicile, or it could develop into a personal diocese.
A Personal Ordinariate is akin to a diocese and people belong to it on account of the particular pastoral reasons for the establishment of the Ordinariate.
As with apostolic prefectures or vicariates apostolic or territorial abbacies, the Ordinary need not necessarily be a bishop, although he could be. Whether or not he is a bishop, the term 'diocesan bishop' in the Code would include him. It is interesting that the CDF's note states that the seminarians of the Ordinariate are to be prepared alongside other Catholic seminarians, which would imply that the Ordinariate would not have its own seminary. We shall have to see, therefore, whether the Ordinary may incardinate priests to the Ordinariate, or what the title of incardination will be upon ordination of a candidate. We shall have to wait for publication of the Apostolic Constitution.
If the Ordinariate can incardinate its own clergy, I would think that such an Ordinariate would enjoy the status of a particular Church as envisioned by Can. 368. (Personal Prelatures are not particular churches.) In accordance with Can. 372/2, particular churches distinguished by the rite of the faithful or some other similar reason can be erected. The similar reason in the current case is the liturgical and spiritual patrimony of those who are currently Anglicans.
It could be, however, that the clergy are incardinated into a currently existing diocese but are dedicated to the Ordinariate, rather like the priests in the military ordinariate in this country. They are diocesan priests who are destined (temporarily or for an indeterminate period of time) to the mission of the military ordinariate.
Importantly, these Personal Ordinariates will be formed in consultation with local Conferences of Bishops. It is the Holy Father who will establish the Ordinariates. The Conference of Bishops will be consulted, but the decision rests with the Holy Father.
The subjects of the Personal Ordinary will, of course, be Catholic. I would assume, therefore, that priests who are not members of the Ordinariate will be permitted to celebrate the liturgy according to the distinctive Anglican liturgical patrimony, e.g. if they are asked to supply in the case of a shortage of priests. Certainly I would imagine that there would be nothing illicit in concelebrating at such a liturgical celebration since the Code permits us to concelebrate at any Catholic celebration of the Eucharist. Likewise, the lay faithful may attend Mass in any Catholic rite. Perhaps there may even be a 'mutual enriching' of the Roman liturgy and the Anglican liturgical patrimony. The note says:
Insofaras as these (Anglican) traditions express in a distinctive way the faith that is held in common, they are a gift to be shared in the wider Church.
This is clearly a very significan moment ecumenically for it is a recognition that the Anglican liturgical and spiritual patrimony belongs to the Catholic Church.
The joint statement of Archbishop Nichols of Westminster and Archbishop Williams of Canterbury is quite amazing. I feel it must have taken a great deal of humility on the part of Williams to join in this statement. We should, I feel, keep him very much in our prayers.
UPDATE: Have just heard the headlines on the midnight news on Radio 4: The Pope has been accused of poaching clergy in allowing anglicans to enter the Catholic Church. Laughable!
UPDATE: Great posts on this issue by Father Finigan and Father Finnegan.