Inferiority complex — what exactly does that mean?

Literal

Inferiority-complex — it [topic-は] exactly what-kind-of thing [question-か].

A two-part structure: a nominal topic set off by an em-dash (Japanese uses ― for this), followed by a self-clarifying question. 正確には ('exactly, precisely') is a set adverbial phrase. どういうことか is the idiomatic 'what (kind of thing) is it?' — literally 'what-sort-of-saying-thing-か,' used to ask for clarification of meaning or implication.