Let $H$ be a Hopf algebra. A Yetter-Drinfeld module over $H$ is a triple $(V, \cdot, \delta)$, where $\cdot : H \otimes V \to V$ , $\delta : V \to H \otimes V$ are actions and coactions respectively, $(V, \cdot)$ is an H-module, $(V, \delta)$ is an H-comodule, and \begin{align} \delta(h \cdot v) = h_{(1)}v_{(-1)}S(h_{(3)}) \otimes h_{(2)} \cdot v_{(0)} \quad (1) \end{align} for all $v \in V$, $h \in H$, where $\delta(v)=v_{(-1)} \otimes v_{(0)}$, $(\Delta\otimes 1)(\Delta(h))=h_{(1)}\otimes h_{(2)} \otimes h_{(3)}$.
I am trying to understand the compatibility condition (1). Where do the compatibility condition (1) come from? Thank you very much.