In this study, we explore the relationship between the complexity of neural networks and the internal compositional structure of the function to be approximated. The results shed light on the reason why using neural network approximation helps to avoid the curse of dimensionality (COD). I will first introduce four compositional features that determine the complexity and error upper bound of neural network approximation for dynamical and control systems. Then, several examples will be given to illustrate the widely observed phenomenon in science and engineering that complicated functions are formed by the composition of simple ones.