Carol Williamson demonstrates herd work on horseback while Brad Barkemeyer explains the techniques and strategies used in herd work competitions. The video explains how riders make clean cuts from the herd, work parallel lines or V shapes with the cattle, and legally quit. It highlights the importance of herd holders, turnback men, and minimal rider movement in keeping the cattle in the working area. The demonstration focuses on cutting a specific cow and managing stray cattle, providing insights into the nuances of this equestrian sport.