Let $X$ be a normal complex variety and $\mu : Y \to X$ a resolution of singularities. We define the relative canonical divisor to be $K_{Y/X} := K_Y - \mu^* K_X$.
In his book Positivity in Algebraic Geometry II, Lazarsfeld mentions in passing (pg.146) that $\mu_* \mathcal{O}_Y(K_{Y/X}) = \mathcal{O}_X$. Why is this true?