What can I say of an $m$-dimensional submanifold $S$ of an $m$-dimensional manifold $M$?

Question

I consider a differentiable manifold $M$ of dimension $m$. Let be $S$ a submanifold of $M$ of the same dimension $m$.

What can I say about $S$?

I have tried to prove that $S$ is open but I get stuck. My idea was to use the inverse function theorem to the inclution $i:M \rightarrow S$.

Any help will be appreciated. Thanks!