A pommel is the rounded knob on a horse's saddle that a rider grips with one hand. The raised front of the saddle itself can also be called a pommel.
Some saddles, particularly the modern western type, have a metal grip at the front, known either as a horn or a pommel. Other saddles don't have this knob, but instead have a raised front edge that's also called the pommel. When pommel is used as a verb, it means "beat or strike repeatedly," a variation on the word pummel. The Old French root is pomel, "rounded knob," from the Latin word pomum, or "apple."