Mirror symmetry is an example of a duality, which occurs when two seemingly different systems are isomorphic in a non-trivial way. The non-triviality of mirror symmetry involves quantum corrections. It’s like the Fourier transform, where “local” in one domain translates to “global”—something requiring information from over the whole space—in the other domain.
Under a local/global isomorphism, complicated quantities get mapped to simple ones in the dual domain. For this reason the discovery of duality symmetries has revolutionized our understanding of quantum theories and string theory.