The Empire was run by the Emperor, aka Darth Sidious, former Supreme Chancellor of the Galactic Republic. He was an evil being who possessed weird and wonderful powers like Force Cackle, which struck fear into the hearts of his enemies.
Not only that, but his apprentice, Darth Vader, was also put in charge of the Imperial Fleet. He is arguebly more terrifying, with his weird breathing and his jet black mask, constantly twisted into on angry expression.
Another key figure in the Empire is Grand Moff Tarkin. Although he was killed during the attack on the First Death Star, his doctrine of power through fear lived on and was the driving force behind the construction of the Second, more powerful Death Star.