Hiring a hero to be your mayor has an effect on your town. It can speed up the time it takes to build structures or train troops. The statistics of your mayor determine how much it speeds up:
Mayors with high Politics (POL) affect the building times of structures, the collecting of resources, and the building times of defenses on your walls.
Mayors with high Intelligence (INT) affect the speed of researching items in the academy.
Mayors with high Attack (ATT) affect the rate at which new troops are trained in the barracks. Strangely enough they don’t affect the speed of building defenses like archer towers.