Quick answer: a pom-pom is a handheld prop made of many thin plastic strips fixed to a handle, used to add visual sharpness and flash to motions, dances and formations - one of the most recognisable pieces of equipment in cheerleading's history.
What It's For
A pom-pom's main purpose is visual: the strips catch light and movement in a way bare hands don't, making motions look sharper and more visible, especially from a distance in a large venue.
How Pom-Poms Are Used
Pom-poms are typically used during specific sections of a routine - often chants and dance breaks - rather than throughout an entire performance, since they're generally set down or handed off before stunts and tumbling, where they'd get in the way.
How Pom-Poms Developed
Pom-poms became closely associated with cheerleading through the mid-20th century, growing alongside the sport's increasing use of organised motions and technique. See History of Pom-Poms for the full story.
Pom-Poms and Motions
Because pom-poms change how a motion reads visually, teams often practise key motions both with and without them, to make sure technique stays sharp and correct even once the prop is added - see Cheer Motions Explained for the underlying arm positions pom-poms are used with.
Related Equipment
See Cheer Bows for another of cheerleading's most recognisable visual traditions.