The wording is confusing mainly due to translation problems (and confusing differences between the Missal and Graduale texts). But what it means no more or less than what has been the Roman Rite standard for ages: the entrance antiphon in Gregorian chant.
It has long been the practice to name the Mass of the day after its antiphon. Some of the better known ones are Gaudete, Laetare, Requiem, Quasimodo, Jubilate Deo, Cantate Domino, and Viri Galilaei.
Today, not one in a hundred Catholic musicians knows this, much less can sing them, which is very sad, because this is a piece of our heritage that is missing from our parishes. Gone too, largely, is even the knowledge that the entrance music does have (and should have) some intimate relationship with the Mass itself.
Part of the reason is the proliferation of the phrase "Gathering Song" to describe the entrance music. I wish I knew where the phrase came from. Perhaps it came from the impulse that many people have that musicians should give people a kick when they get in the door, let them know that Church is a fun and happy place, make people glad that they are together with each other.
But here is the problem. It is a sociological fact that the primary reason Catholics go to Mass is not to see and be seen. They don't choose their religion in order to be adopted into a "community." They certainly don't go for the music. The Holy Sacrifice is the reason, and even if people don't entirely understand that explicitly, the idea that we are there for deeper reasons than social ones is a pervasive understanding even today in the Catholic Church. A chipper, welcoming song just doesn't connect with the Catholic sense.
What happens is this. People arrive and kneel to pray. There is usual a sense of quiet and this is very much to be valued. Suddenly the music begins, and you are called on, and sometimes badgered incessantly, to pick up your hymnal and sing and sing. It goes on for a few verses, and the mood is transformed dramatically and decisively from penance and quiet to loud celebration. Then it stops. The priest is at the altar, though you didn't see him get there, since your head was buried in a book. The penitential rite begins. The shift is too dramatic. You have time for neither authentic celebration nor authentic penance, and this is vaguely annoying.
The phrase "gathering song" really must be completely retired from use. "Gathering song" implies that Mass is something like a family reunion, a dinner party, a staff meeting, or some other people-center event in which people just sort of show up and enjoy each other's company. This is decidedly what Mass is not. The Mass is the great miracle. As a symbol of what is taking place, the position of the people is in procession as led by the priest to the altar and toward the East of the risen Christ. We are not "gathering" but spiritually processing toward the focal point at the center.
In any case, the phrase "gathering song" is not mentioned the defunct and otherwise highly misleading American document "Music in Catholic Worship." It is not in the General Instruction. It is not in the Missal or any rubrics that I can find. In fact, the GIRM says specifically that "after the people have gathered, the Entrance chant begins…"
There is a sense, then, in which phrase "processional hymn" is actually better. But to press the point further, we should take note that the music chosen for this processional is not just arbitrary. It is rooted deep in history, and there is usually a good rationale for thing such as this.
In the practice of the ages, the introit from the music of the Mass is sung by the choir alone. The people do not sing. Is this a bad thing? Apparently many people think so. But they should consider that the Introit connects people to both their heritage and to the liturgical day. The music is also beautiful. It facilitates prayer. And it enables the people to actually watch and thereby better experience the procession itself.
Another option is to choose a very simple plainsong piece sung to the entrance text, in Latin or in English. The people can respond at the Gloria Patri, without having to dig around in some book or program. Or they might just want to continue the sense of prayer without singing. The sense of contemplation and reflection are maintained. There is no interruption between the pre-Mass prayer and the penance rite.
Many Catholic musicians, recently enlightened about the existence of the propers, have come to the view that this approach is far better than the "gathering song" approach to the beginning of Mass. But their pastors or liturgy teams are prohibiting a change. They have some sense that the people expect to sing a hymn, not listen to the proper text sung. They fear making the change because it might prompt some sort of backlash.
The experience at our parish, however, suggests that this "pastoral" consideration is completely unfounded. It is not necessarily the case that people come to Church with the goal of ripping into a big and loud welcoming hymn just as soon as possible. It is sometimes a welcome relief not to have to sing but rather being granted time and space to look and listen; indeed, the lack of an imposed obligation to vocalize can enhance interior participation.
Pastors: please let your musicians try an entrance with the proper of the day and see what happens. The people gathered will, for the first time, watch as the procession takes place. Because of the fitting nature of the proper text, the "homiletics" of the day--which can be of a higher form that mere didactic teaching of a lesson--can begin long before the readings and the sermon.
The Roman Rite is not structured to have two bookends on either side, one called the Gathering Song and the other called the "Sending Forth" (to bring up yet another absurd phrase that has entered into our liturgical language). So far as I can tell, both phrases are complete inventions with no precedent and no liturgical basis whatever. Let the Roman Rite be the Roman Rite. This is part of what it means to trust the liturgy to do what it is structured to do.