The thaum is the basic unit of magic. Enthusiastic students together with Ponder Stibbons have found out that the thaum is made up of so called resons (lit. thing-ies), which are themselves made up of at least five flavours (including up, down, sideways, sex appeal and peppermint). One thaum is defined to be the amount of magic which is needed to create a white pigeon or three billiard balls.
Another project related to the thaum is Ponder's Thaumic Reactor, designed deliberately to split the thaum and generate massive amounts of energy. As Ponder says, the energy that would be generated by such a thing would be enough to send the entire university to the moon. Or create a universe...
Currently, there are attempts to replace this unit with a newer unit of magic: the prime (which is apparently a "metric" unit, since Rincewind refers to milliPrime in The Colour of Magic). This has unfortunately not caught on among the older wizards, in much the same way that certain Britons and Americans on Roundworld still prefer the Imperial system of measurement to the Metric.
The atom, long thought to be the smallest unit of which all matter is composed, was later found to consist of protons, neutrons, and electrons. These were later found to contain quarks in six flavours: up, down, top, bottom, charm and strange. This makes about as much sense (those particle physicists, eh?).
And res is Latin for “thing.” Resons, eh?