The term 'trot quickly' can be summarized as running at a fast pace. It is a type of gait that is faster than a walk but slower than a gallop. Trotting quickly is often used in horse riding, where the horse moves its legs in diagonal pairs, with the left front and right hind legs moving together, followed by the right front and left hind legs. It is also used in running, where it is a form of jogging.