A smooth domain $\Omega$ is an open and connected subset of the whole domain, say $\mathbb{R}^n$, of which the boundary $\partial \Omega$ is "smooth".
The smoothness of the boundary, intuitively speaking, is:
The boundary of a smooth domain can be viewed as the graph of a smooth function locally.
My question is, why is the smoothness of $\partial \Omega$ related to the function smoothness? Can I have pls a simple example or explanation?