What does "Altare privilegiatum" mean exactly today?

Are the indulgences attached to privileged altars still valid?

The short answer is no.

A Privileged Altar (Altare Privilegiatum) is an altar in a Roman Catholic church where a plenary indulgence can be gained for a soul in purgatory whenever Mass is celebrated there.

Two examples are the Vallarpadam Church, Kerala and St. Thomas of Canterbury Church, Canterbury.

The term 'Privileged Altar' is used in the 1917 Code of Canon Law. The plenary indulgence is attached usually by the celebration of a Requiem Mass and benefits a soul in purgatory when Mass is offered for that intention at the Privileged Altar.

The grants of privileged altars were suppressed by Norm 20 of Pope Paul VI's Apostolic Constitution 'Indulgentiarum Doctrina'. - Privileged Altar

In Pope Paul VI's new rules for indulgences were published in his Indulgentiarum Doctrina he states the following:

Transitional Norms

These new norms regulating the acquisition of indulgences will become valid three months from the date of publication of this constitution in the Acta Apostolicae Sedis.

Indulgences attached to the use of religious objects which are not mentioned above cease three months after the date of publication of this constitution in the Acta Apostolicae Sedis.

The revisions mentioned in n. 14 and n. 15 must be submitted to the Sacred Apostolic Penitentiary within a year. Two years after the date of this constitution, indulgences which have not been confirmed will become null and void.

We will that these statutes and prescriptions of ours be established now and remain in force for the future notwithstanding, if it is necessary so to state, the constitutions and apostolic directives published by our predecessors or any other prescriptions even if they might be worthy of special mention or should otherwise require partial repeal.

Given at Rome at St. Peter's on January 1, the octave of the Nativity of Our Lord Jesus Christ, 1967, the fourth year of Our Pontificate.

I have personally been in churches where these once called privileged altars still exist and the local clergy had told me the the indulgences pertaining to the deceased had been suppressed. In other words, these once called privileged altars have lost their privileged status and are simply altars or main altars whichever the case may be for a particular church altar.

It is interesting to note that certain priests carried this privilege with themselves, regardless if they offered a requiem mass on privileged altars or not. The privilege was attached to their person!

The 1917 Catholic Encyclopedia has this to say about privileged altars as they existed prior to Vatican II:

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.

Although these ecclesiastic privileges no longer exist, Pope St. Paul VI makes note of the formatting in his Apostolic Constitution Indulgentiarum Doctrina:

n.20—Holy Mother Church, extremely solicitous for the faithful departed, has decided that suffrages can be applied to them to the widest possible extent at any Sacrifice of the Mass whatsoever, abolishing all special privileges in this regard.