The Discworld, of course, operates on magic. Magic flies the Turtle, spins the Disc and reclaims the Rimfall; it's natural and normal and unremarkable. What sometimes perplexes people is the odd way in which things sometimes happen without apparent magical influence. These inexplicable phenomena are given the collective name quantum. The Wizards have created a model universe in which everything is governed by quantum, and there is no internal magical influence and no Narrativium.
Archchancellor Mustrum Ridcully uses the term dismissively as a catch-all phrase summing up all he finds distasteful and annoying in this new-fangled magic they're "discovering" and "inventing" in the High Energy Magic Building at Unseen University. "Hooray," he mutters, sourly, "here comes another bloody quantum..."
In physics, a quantum (plural: quanta) is the minimum unit of any physical entity involved in an interaction. An example of an entity that is quantized is the energy transfer of elementary particles of matter (called fermions) and of photons and other bosons. The word comes from the Latin "quantus", for "how much". Behind this, one finds the fundamental notion that a physical property may be "quantized", referred to as "quantization". This means that the magnitude can take on only certain discrete numerical values, rather than any value, at least within a range. There is a related term of quantum number.
A photon, for example, is a single quantum of light, and may thus be referred to as a "light quantum". The energy of an electron bound to an atom (at rest) is said to be quantized, which results in the stability of atoms, and of matter in general.
As incorporated into the theory of quantum mechanics, this is regarded by physicists as part of the fundamental framework for understanding and describing nature at the infinitesimal level, for the very practical reason that it works. It is "in the nature of things", not a more or less arbitrary human preference.