Score Function Sleight of Hand

REINFORCE turns $\nabla_\theta E[R]$ into $E[R \cdot \nabla_\theta \log \pi_\theta(a|s)]$ by rewriting $\nabla_\theta \pi(a|s)$ as $\pi(a|s) \cdot \nabla_\theta \log \pi(a|s)$. What is this identity called, and why is it essential to the algorithm?