A region commander of the Empire (in the Star Wars universe). A Moff might command a couple of star systems, technically referred to as a region. There were Moffs long before there were Grand Moffs, reporting directly to the Emperor(control freak as he was), but after Moff Tarkin suggested that a higher level of control be asserted to handle the problem of raiders, rebels, pirates and smugglers escaping into another Moffs region when hunted, he was rewarded by being appointed the first Grand Moff.
(Source: The Star Wars RPG)