Question is as in the title.

Why study orbifolds?

I study orbifolds as locally compact Hausdorff spaces $X$ having an orbifold structure, i.e., there exists an orbifold groupoid (proper foliatio. Groupoid) $\mathcal{G}$ and a homeomorphism $|\mathcal{G}|\rightarrow X$, where $|\mathcal{G}|$ is orbit space of the groupoid $\mathcal{G}$.


Let $G$ be a Lie group acting smoothly on a manifold $M$. If one further assumes the action is proper and free then, the quotient space $M/G$ has a manifold structure.


One reason why I find orbifolds interesting is, loosely, if I ignore the condition that the group $G$ (compact Lie group) freely and impose that it only acts almost freely, then there is still some interesting structure on the quotient space $M/G$, i.e., of orbifold.

I don’t know any other places where one would see Orbifolds and how it would be interesting. 

Correct me if I have a wrong understand and share your opinion of how to see an orbifold.

Edit : Wikipedia page does not say anything about groupoid way of looking at orbifolds.