I had always (or at least, for as long as I can remember) known that there are 8 modes in chant, and that the Gloria Patri for the Introit was chosen based on the mode of the Introit.
I had even known that the modes were identifiable based on the final note of the piece and one or two other clues (but primarily, by the number printed at the start of each piece, for practical purposes).
But these had been isolated bits of knowledge, with little understanding and therefore of little use.
What Christopher Hodkinson (of the Cambridge Schola Gregoriana) made clear was the connection between pieces in the same mode; and more particularly, pieces of the same liturgical use (Introit, Gradual, etc) in the same mode. He referred to these as family groups.
Thus, if one is faced with learning a new Introit, for example, a valuable starting point is to note which mode it is in, and then, using the index in one's Liber, look at other Introits in the same mode (which is why, I now realise, the index of the Liber is arranged in that way: all the Introits together first, and each preceded by the number indicating which mode it is in.)
Flicking through these, one can normally find one that is similar to, or at least has similar phrases to, the new Introit one is endeavouring to learn. If one has sung it before, that makes the new one much easier; it also makes the whole task of learning a repertoire much more conceivable: rather than learning all the hundreds of Introits in the Liber individually, one can learn a few typical mode 1 Introits, and so on.
To see (and better, hear) this in practice, compare the two mode 2 Graduals below. Justus ut palma florebit is an archetypal mode 2 Gradual; if you recognise it, without ever having heard it before, it may be because, like me, you are more familiar with the Gradual from the Requiem Mass, Requiem aeternam.
Justus ut palma florebit
For the record, here is the scheme for classsifying Chant into Modes:
Mode 1: Final: Re, Tenor (Reciting note): La
Mode 2: Final: Re, Tenor: Fa
Mode 3: Final: Mi, Tenor: Do
Mode 4: Final: Mi, Tenor: La
Mode 5: Final: Fa, Tenor: Do
Mode 6: Final Fa, Tenor: La
Mode 7: Final Sol, Tenor: Re
Mode 8: Final Sol, Tenor: Do
The odd numbered modes tend to have a range mainly above the Final, and are known as authentic; the even numbered modes tend to have a range both above and below the Final, and are known as plagal: hence the different reciting notes.