What effect does flexibility training have on my basketball game skills?

Flexibility ensures that you maintain optimal mobility of all your joints.  This increases the balance between muscles that will ensure efficient movement and force production.  Also, certain muscular restrictions make it hard to maintain body positions that are essential to your performance.  For example, tightness in your lats (your large back muscle) can prevent you from being able to hold or reach your arms straight over your head, and tightness in your calves may result in a player "fading away" rather than leaning forward when making a move to the basket.