--Hopefully this question does not dublicate another--

In this question Tom Goodwillie pointed out, that the 'atlas part' of the definition of a smooth manifold can be redefined in terms of sheaves. How is that done?

I assume it is something along the line: "An atlas is a sheaf on the site of cartesian spaces (the site with objects $\mathbb{R}^n$, such that ..."

Can someone clarify this point?