Satan is the supreme overlord of hell and the father of the demon race.
Appearance
Personality
From what is seen, Satan is a serious individual and even selfless (having sacrificed himself to stop Bahamut).
It can be presumed he is malevolant in nature.
Plot
Satan and others (Lucifer etc) rebelled against Heaven and the angels who fought back were defeated and thrown down to the earth, to be consumed in the fires of hell, but then they were reborn. The ruler of hell then waged a bloody war with all the gods and living creatures. The last known appearence of Satan was 2,000 years ago, He and other Gods met with the mighty Bahamut and fought him at Aboth. He also sacrificed himself via turning into a god key to seal away the incredibly dangerous Bahamut. He in essence lived on within Amira as she was connected to his god key. He was not forgotten by his kind and is often referenced by many demons (like Beezlebub) and others.
Power & Abilities
There wasn't much displayed for Satan but he did appear to be a deity of incredible magnitude. In the fight with Bahamut, Bahamut almost seems further enraged in his presence. Satan and Odin were two of the only gods who did not flee from Bahamut, Satan exhibited immense power when unleashing upon Bahamut. This was to the point where he and Odin could stop the beast Bahamut temporarily. .
Trivia
Although Satan is referenced as the original lord of hell, The creator of the series made Lucifer and Satan with reversed roles in regards to typical Christianity. Lucifer is the ruler of hell (a fallen archangel with a power near equivalent to God's) whilst Satan is Lucifer's son (the Antichrist). In some texts Satan and Lucifer are the same entity. However this is not displayed within the show.