Satan is the father of the Antichrist, Adam Young.
Satan is the original demon; he led the rebellion against Heaven and was responsible for forming Hell (as an organisation, if not a place) when the rebel angels were made to Fall.
Satan is the ruler of Hell, though he apparently does not have much to do with the organisation and running of Hell, at least in relation to Earth, due to his rare appearance in the series.
Significance in series Edit
After Adam refuses to trigger the End of Days, despite Beelzebub's and Gabriel's attempts to persuade/bully him into it, the two supernatural beings depart to inform Adam's father, Satan, of Adam's disobedience. Minutes later, the earth begins to tremble as Satan ascends. Crowley and Aziraphale manage to speak to Adam right before Satan appears, encouraging him to use his power over reality to defeat - but not fight - his father.
Satan makes his entrance, demanding to know where his son is. When Adam comes forth, Satan (ironically) scolds him for rebelling. Adam, unaffected by Satan's words, uses his power to declare that Satan is not his father, pointing out that he was never there as a parental figure in Adam's life. This declaration results in reality being changed, with Satan no longer being his father, Adam no longer being the Antichrist, and Adam's adoptive father (now his real one), Arthur Young, appearing instead. This alteration of reality officially puts a stop to Armageddon.