Any foreign country whose internal or external politics your personal superpower (like, say, the US) does not agree with.
The word is used to whip into a frenzy the bloodthirsty
masses of justifiedly enraged citizen/voters, so that the
subsequent carpet bombing of said rogue state does not
come as a surprise: rather, a natural consequence of the
state of things.
The words "rogue state" indicate clearly that foreign policy is spinning into motion: that's why they are rarely
heard in countries that, like Italy have no foreign policy (and, for the matter, few policies) at all.