The cat stance is all about mobility. Commonly the back leg is coiled while the front leg uses the ball of the foot to maintain some equilibrium. This allows for any weight shift to push the practitioner in some direction without any foreshadowing. As such the stance is best when it is responding to power. The evasion and counter attack are initially most effective from this stance. Obviously, with practice and training anything can be done from any stance. The physical posture and alignment of the bones causes direction changes and focuses on speed to be most efficient. Most styles which will focus the cat stance into specific directions through specific block/attack combinations or leaning. Those styles/people which train this stance allot also tend to focus on evasion and footwork. Other styles will train this stance as a transition between the other stances and as a kicking base. When done precisely, the cat stance causes a 45 degree shift in direction. When turning, it does not matter if you pivot on the heel or ball of the foot. Most people switch between both anyway. Often the kicking techniques will cause one pivot to be used exclusively but if the kicks are not trained well then it doesn't matter. It is not used in Chi Kungs until the very advanced levels and tends to be glossed over as a basic stance. Often the third stance taught.
That is about all. Nearly everything else that can be said requires tactical skill and is beyond the basic level that this article is concerned with.