Moff was the grandiose title given to the governors of star systems and sectors during the Galactic Empire. Appointed by Palpatine himself, they were intended to be loyal instruments of his will. However, most of them ended up turning into either fat slobs without a lick of sense (and end up deposed by the Rebels), or conniving sons-of-banthas who would sell their own mothers for loot, power, or other fetishes (the most brazen of which often faced retribution).
After the Empire was reduced to its pitiful remnants, the title of Moff continued to hold import, though the number of Moffs in power had been drastically reduced.
Moffs were never, ever to be confused with muff divers.