What is the meaning of Diffeology?

The set of smooth parametrizations of a given set ${\displaystyle X}$; the set of smooth maps ${\displaystyle S\rightarrow X}$, where ${\displaystyle S}$ is any open set ${\displaystyle \subseteq \mathbb {R} ^{n}}$; the theory of such constructs.

Source: wiktionary.org