The ruler of Hell oversees the realm. He is responsible for controlling over demons and ensuring damned souls get punished. He must also patrol the gates, making sure damned souls do not escape.
The first ruler of Hell was the angel Lucifer Morningstar, who was cast out of Heaven as punishment for rebelling against his father, God. Lucifer reluctantly ruled over Hell for many eons, before deciding to abdicate his throne and leave Hell for Earth.
In Lucifer's absence, Amenadiel was forced to run Hell, a job he loathed. Amenadiel tried numerous times to convince Lucifer to go back to Hell but was unsuccessful.
Lucifer had suggested to his mother, the Goddess of all creation, to become the new ruler of Hell as opposed to her original plan to return to Heaven.