I think I got the answer now. The main idea is this: When we gauge continuous symmetries we identify all the states $$A^\mu=A^\mu+\partial^\mu\chi$$ (which are continuously many) as a unique physical state.

When we gauge a discrete symmetry (let's assume it's generated by $\theta$) we identify all the states
$$|\Psi\rangle=\theta^n|\Psi\rangle$$
where $n=1,\ldots N-1$ and $N$ is the order of the discrete symmetry group. So we identify a finite number of states as a unique physical state. This is exactly what we do when we are orbifolding.

This post imported from StackExchange Physics at 2014-03-31 16:01 (UCT), posted by SE-user Heterotic