Cat Crosses the Courtyard is not so much a sword form but a method of movement.
Cat Crosses the Courtyard is a way of carrying oneself which maximizes alertness and reaction potential. The blademaster lets his body hang relaxed, spine straight, as though suspended by a line. It affects a self-assured manner and projects confidence, but could also be described as a relaxed, almost arrogant saunter.
Lan Mandragoran instructs Rand al'Thor to assume this walk during his first meeting Siuan Sanche, the Amyrlin Seat. Rand later dropped into this walk while talking with Lord Barthanes Damodred at his estate. Eamon Valda sauntered into the dueling ground with this walk after being challenged by Galadedrid Damodred.
The real-world parallel appears in many traditional martial arts where students are taught to move with the spine straight in order to maintain balance and body structure while staying fluid and relaxed. The Japanese kensei, Miyamoto Musashi wrote in The Book of Five Rings, "make your everyday walk your warrior's walk" as a sly reference to this kind of training.