On a recent trip to Old St. Mary's in Cincinnati, Ohio I noticed the high altar had the word "Altare Privilegiatum" or "Privileged Altar" on the front.
The Catholic Encyclopedia written in 1907 describes what a privileged altar means:
An altar is said to be privileged when, in addition to the ordinary fruits of the Eucharistic Sacrifice, a plenary indulgence is also granted whenever Mass is celebrated thereon, the indulgence must be applied to the individual soul for whom Mass is offered. The privileged altar must be a fixed, or immovable, altar, but in a wider sense that is, it must be stationary or permanent, whether built on a solid foundation or attached to a wall or column, even though it be not consecrated, but have merely a consecrated stone (portable altar) inserted in its table. The privilege is annexed not to the altar-stone, but to the structure itself, by reason of the title which it bears, that is, of the mystery or saint to whom it is dedicated. Hence if the material of the altar be changed, if the altar be transferred to another place, if another altar be substituted for it in the same church, provided it retains the same title, and even if the altar is desecrated or profaned, the privilege is preserved. To gain the indulgence, the Mass must be a Mass of Requiem, whenever the rubrics permit it. If, on account of the superior rite of the feast of the day, or on account of the Exposition of the Blessed Sacrament, or for other reasons, a Requiem Mass cannot be celebrated, the indulgence may be gained by celebrating another Mass (S. C. Indulg., 11 April 1864). This privilege is of two kinds, local or real and personal. It is local or real when it is annexed to the altar as described above. Hence whoever the priest may be who celebrates Mass at such an altar, the indulgence is gained. It is personal when it is inherent in the priest, so that it does not depend on the altar, but on the priest who celebrates. Hence on whatever altar he may celebrate, whether it be a fixed or a portable one, and in whatever church he celebrates, the altar he uses is for the time being a privileged altar. On 2 November every altar is privileged. The bishops of the United States have the faculty (Facultates Extraordinariae C., fac. viii) of declaring privileged one altar in every church and public chapel or oratory, whether it be consecrated or not, of their dioceses, provided this privilege had not been previously granted to any other altar in such church under the same conditions.
This benefit of a privileged altar was also granted to certain priests where they celebrated Mass at and at least one of those instances was for priests who made the heroic act of charity. As the Purgatorian Manual states: "The Indult of a Privileged Altar, personally, every day in the year to all priests who shall have made this offering."
To summarize: A privileged altar is an altar where a plenary indulgence could be applied in favor of a particular soul in purgatory by the priest celebrating Holy Mass whenever Mass was celebrated there. This was an indulgence, over and above the graces and benefits normally flowing from the celebration of Mass. The “privilege” was attached to the place, not to the physical altar, and the privilege could also be given to a certain priest so that no matter where he celebrated a plenary could be gained!
Sadly, Paul VI removed these privileges and countless other indulgences in 1967 in Indulgentiarum Doctrina. However, the validity of his actions remains questionable by some and, despite this, we should never stop having Masses offered for the dead and gaining indulgences for the faithful departed, especially during the month of November.