The Eighth Archduke looks like the classical fictional devil: red, big, horned, winged, clawed, fire-cloaked, still kinda handsome, and so on. As the second most powerful devil of Baator, there is only one way for the Lord of the Eight to go upwards: he has to overthrow Asmodeus himself. Nearly every moment of his existence is spent plotting towards this end. He is a being of pure ambition and avarice, incapable of satisfaction with anything less than supreme power over Hell itself. He is currently the steward of the only known permanent planar portal into Nessus, commanding the armies that protect the gates into the last layer of Baator with his vast armies of Ice Devils and Pit Fiends. Because of this limitless ambition, he has alienated himself from all but a few archdukes. One of his few allies is Dispater, with whom he has an alliance that dates all the way back to the days of the founding of Baator.
Mephistopheles' ego is his biggest flaw. He sees himself as the rightful ruler of Hell, superior to all of his peers. He especially hates Baalzebul, seeing him as a pretender and no "true devil," since the latter is a fallen archon. He also sees the Lord of Lies as a threat to Asmodeus, and thus a threat to his own inevitable lordship over Baator. The Lord of the Eight does not really have a strong cultist presence on the Material Plane. Mortals often confuse him with Asmodeus, which rather infuriates Mephistopheles. Why Asmodeus puts up with Mephistopheles is unknown, but it is possibly because of a devil-you-know scenario, or because his struggle with Baalzebul keeps Asmodeus' position more secure, or because he figures that no matter who became Lord of the Eighth they, devils being what they are, would spend the rest of eternity trying to overthrow him. It also must be noted that Mephisopheles has previously betrayed and destroyed rebellions among the other dukes to overthrow Old Scratch, presumably because he wants the job for himself, intact.
If you've been paying attention you'll note that Mephistopheles is almost literally a transplant of Starscream from Transformers to D&D. He checks literally all of his characterization boxes except the screechy voice.
In a bid to increase his power, he has also developed a unique Hellish magic, simply called Hellfire, which has the unique ability to bypass any amount of fire resistance or fire immunity, as it is not merely magical fire but instead powered by the primal energy of the Nine Hells. By calling himself a "God of Hellfire" and gifting mortal servants, unwitting or otherwise, with access to this magic he is banking on getting a steady supply of souls to his layer, because as a certain other fictional universe knows, there's always war going on somewhere in the multiverse and therefore no lack of combatants wanting for effective weapons and offensive magic. The creation of Hellfire and highly destructive constructs using it known as "Hellfire Engines" has also indirectly bolstered the forces of the Nine Hells in the Blood War, because Hellfire will reduce virtually any Demon to smoldering cinders just as easily it would a Fire Elemental (fancy that). For some reason Mephistopheles has also seen fit to use Hellfire for mundane heating purposes on his home layer of Cania, which just happens to be the coldest layer of the Nine Hells, so cold that the weather outside of the "warm zones" he's created will freeze non-Devils without cold immunity or a special permit from Mephistopheles protecting travelers from Cania's hellishly cold weather (but not cold damage of any other kind) solid within minutes. It's gotten to the point that many of his Ice Devil servants have deserted his warm abode on Cania and are trying to work their way back into his good graces by coming up with an offensive cold spell more to their liking than "distinctly un-Canian fire magic."
Mephistopheles also had a pretty big part in the Hordes of the Underdark campaign in Neverwinter Nights, where he was the BBEG (not really a spoiler), and gets a lot of interesting backstory. He has a pretty cool, semi-original plan to beat Asmodeus that is, naturally, foiled by a PC and his gang of badass heroes.
|The Archdukes of Hell|
|Avernus||Bel or Zariel|