。
My mother let me go to the movies.
Literal
Mother [topic-は] I [subject-が] movie [to-に] go [nominalizer-の] [object-を] permitted-[benefactive-てくれた]
許してくれた = 'permitted (for my benefit).' てくれた layered onto 許す flags the permission as a favor received by the speaker, not just a neutral grant — an emotional shading that simple 許した would miss.