A member of a cheerfully anarchistic desert tribe in Klatch who will fight anyone on general principles. Think of the Nac Mac Feegle in flowing desert robes, and you have a good idea of their general temperament.
The concept of D'Regness is discussed at greater length in Jingo, where their opposition to being a part of anyone's Empire, or any part of a set-up where taxes and loyalties are expected to be paid, is crucial to the development of the story.
They have very strict ideas about women fighting: they expect them to be good at it. It is generally said that if a D'reg is your friend he is your friend for the rest of your life, and if he is not your friend the rest of your life will be about five seconds; to still be alive five minutes after meeting a D'reg tribe is a clear indication that they really like you. Distrust is generally encouraged among the D'regs, with 71-hour Ahmed once telling Vimes that his mother would be greatly offended if he trusted her on the grounds that she would feel she hadn't brought him up properly.
In Jingo, Samuel Vimes made friends with them unintentionally by the dangerous expedient of giving their (then) leader an Ankhian Handshake. This committed them to (i) a change of leader, as anyone foolish enough to let himself be taken in like that couldn't have been worth following; and (ii) seventy-two hours worth of hospitality extended to Vimes's 'regiment'.
This is a crucial seventy-two hours, as the D'Regs are quite prepared to transfer their loyalties to a leader (Vimes) who is mad enough to be not only hopelessly outnumbered, but to charge both sides simultaneously, as they manoeuvre into battle. (This is helped by 71-hour Ahmed innocently confusing the words of command which a camel understands as "Speed up!" and "For Gods' sake stop!")
The name D'reg is a combination of Roundworld's Tuareg nomadic Arab peoples, who are generally warlike when antagonised, and Dreg as in the "dregs of humanity" - dregs, for non-English speakers, being the horrible bits left at the bottom of a cup of coffee, tea or barrel of beer: the worst bits.