Fauxbourdon or faux bourdon is, as Fr. Thompson said, a 15th Century practice involving one voice singing a perfect fourth below the cantus firmus, and another part played or sung in sixths below, although the lowest part is often rhythmically independent of the upper two, making the counterpoint more interesting. It could be done as a simple harmonization of a chant, but is not usually used for harmonization of psalm tones; Dufay is said to have invented faux bourdon and used the technique frequently, writing short faux bourdon pieces in which the bass is instrumental, and longer pieces with faux bourdon sections.Ignacio recommends: Ensemble Organum's "Messe des Invalides" and "Corsican Chant"
There is an English practice with a similar name--faburden--which is more often associated with improvisation and the kind of psalm-tone harmonization heard here. Faburden involves one voice singing a a fourth above the chant, and one voice singing thirds and fifths below the chant (he must begin and end on a fifth, and never sing two fifths in a row, but may sing as many thirds as he likes).
A third practice with a similar name is falsobordone, an Italian practice of harmonizing psalm tones in four parts, with root-position triads and the chant in the top voice.
This is confusing, I know--it took me a semester-long seminar on 15th Century counterpoint to sort it all out. I think I hear a voice singing higher than the cantus firmus in that video, which means that this schola is singing faburden rather than faux bourdon or falsobordone, since faburden is the only practice in which a voice sings harmony above the chant.
References to 'faux bourdon':
Guillaume Dufay: The Man & His Works
Faux-bourdon - Wikipédia
Largement utilisé pour chant sur le livre, le faux-bourdon se ...
JSTOR: Guillaume Dufay's Concept of Faux-Bourdon
Fauxbourdon - Wikipedia, the free encyclopedia