The posture ad orientem is often used not to mean facing literal east but facing the apse or wall behind the altar, with priest and people looking in the same direction, even if they have their backs to the actual direction east. To put it simply, ad orientem is when the priest always faces the altar, the same direction as the people face, whether or not the altar is against the wall or freestanding.
The opposite of this is called versus populum, in which the celebrating priest faces the people (at least during part of the liturgy, most generally during the Eucharistic liturgy). For this the altar must be free standing and have room for the priest and other assisting ministers to stand "behind" it as they face the assembled people.
In effect both terms are somewhat misleading. It is not about the priest facing the people or the wall but about a liturgical east which has supplemented the actual orientation toward the east. When the priest faces the people, it is more correct to say he faces liturgical east. So at St. Peter's in Rome the Pope faces the people because the building faces west and for him to face east is to face the people.
In the earliest days of the Church, the Eucharist appears to have been celebrated on portable altars set up for the purpose. Some historians hold that, during the persecutions, the Eucharist was celebrated among the tombs in the Catacombs of Rome, using the sarcophagi of martyrs as altars on which to celebrate. When Christianity was legalized under Constantine the Great, formal church buildings were built in great numbers, normally with free-standing altars in the middle of the sanctuary, which in all the earliest churches built in Rome was at the west end of the church. This did not mean that priests faced the people but this did allow for censing the altar on all sides. The Eastern Churches maintain a freestanding altar but celebrate ad orientem. As the sacrificial understanding of the mass predominated, so, it seems, did the altar move further back until it was against the wall, at least this is what some have postulated.
The present-day Roman Missal does not forbid the ad orientem position for the priest when saying Mass and provides that new or renovated churches make possible the facing-the-people orientation (versus populum): "The altar should be built apart from the wall, in such a way that it is possible to walk around it easily and that Mass can be celebrated at it facing the people, which is desirable wherever possible." For this reason many beautiful and massive stone and wooden high altars were virtually abandoned following Vatican II and a cheap, ugly, and insignificant little table placed in front of the "high altar" to allow for versus populum orientation.
Rome faces the odd circumstance that in some ancient churches the ad orientem position is physically impossible, and in others it is impossible for the priest to face the people throughout the Mass. When Benedict XVI celebrated ad orientem in January of 2008 the fire for the return to ad orientem and to the Latin mass was kindled even more. It is customary for this Pope to celebrate versus populum and yet the altar is set with candles and crucifix between the celebrant and the people. Rome is filled with the buzz over a return to Latin in regular use, with heated discussions over orientation, as well as a host of other liturgical issues. But Rome is not the only place where this is all the buzz. Lutheranism is also rethinking the orientation of the priest.
For the Lutheran this involves the discussion of the sacrificial and sacramental acts in the Divine Service. The all sacrificial acts are directed to or speak to God and therefore are said facing the altar. The sacramental acts (God addressing us) are said facing the people. The sacrificial parts of the liturgy are generally agreed to be the invocation, confession of sins, introit, kyrie, gloria, collect, gradual, creed, offertory, intercessions, proper preface, sanctus, our father, verba, nunc dimittis, post communion collect. The rest are sacramental where the pastor faces the people -- except for the elephant in the room, the Verba. There has been more than a little ink spilled over the historic designation of the Words of Institution as sacrificial, that is, prayer or prayed proclamation. Rubrics tell us in the pastor faces the altar for the consecration.Some would suggest that this is not a question of turning your back to the people but all facing the same direction during prayer.
Brother Weedon said once: Finally, about those free-standing altars. Luther early on expressed a preference for them and for the pastor facing the people from behind them. But the Lutheran Church largely ignored his preference and until the 20th century most Lutheran altars were against the east wall and the pastors faced them whenever a "sacrificial" part of the service took place.
I grew up ad orientem, both churches I attended during college and seminary and both parishes I have served are versus populum (including Redeemer Ft. Wayne under Fr. Evanson). Quite frankly, I cannot get excited about this argument. It is with not a little amusement I read the dripping commentary from Rome and I am saddened to say that some Lutherans have begun to make this a big issue and addressed it in the same biting way. Just like those who are convinced the Common Service (TLH style) is the ONLY legitimate Lutheran liturgical expression and the the other Divine Service formats of LSB are less than legitimate. I cannot get excited about this debate either. I am interested in the legitimate theological perspectives which shape the discussion on both sides -- just not convinced that it is worth becoming as entrenched in this debate as is Rome (and, by extension, its brouhaha over Novus Ordo or Extraordinary Form). I love Latin, too. But I am not thinking that Latin needs to be reintroduced as the language of the mass. Surely all would agree that the English translation of the Roman mass is abysmal but that could be corrected without returning to Latin. If there are errors in the way that free standing altars are used among Lutherans, surely they can be addressed without tearing them out and restoring the altar against the wall. At least, that is how I see it...