The cat stance gets its name for being able to spring forward like a cat. Right foot is pointing to your right (or to your right 45°) with 85%-90% of your weight on the right leg (knee bent sitting low), the left heel is a foot width away from your right heel, resting on the ball of your left foot (Left Cat Stance). The Cat Stance is a transitional stance, meaning it is a stance in between other solid stances. When you half moon forward, you shift your weight basically moving into a cat stance before finishing the step into the half moon stance. Because of the weight distribution of this stance, your lead leg is ready to kick (making it a fraction faster), and with most of your weight on the back leg, you have ready explosive power for a leap or spring forward.
This stance helps strengthens the legs.