Yawgmoth was (and to many hopefuls, including myself, is) a Thran who also happened to be the guy behind the original Phyrexia. TL:DR, he was a god, who had a whole plane of existence to call his own. Said plane of existence quickly became known as the Phyrexian Empire, with the signature "thing" as hordes of bio-mechanical warriors, demons, and monstrosities (Think a more grimdark AdMech with some sorcery thrown in, and you'll have a general idea) He also tried to take over Dominaria a few times (I think it was three) and kept doing evil things until he was killed by Urza and an alliance of planeswalkers. This is a very simplified explanation but should suffice in a pinch.
The key part about Yawgmoth is that he was absolutely not a planeswalker, but merely was a completely mortal genius who managed to elevate himself to become the single most powerful creature in the history of Magic:The Gathering, even in the era of pre-mending planeswalkers. By strategically making friends he managed to gain control over an entire universe, then, when he was trapped, he spent millennia planning and plotting his return, before leading a full scale invasion of the whole of Dominaria (i.e. super massive plane), and was defeated in the climax of the single largest plot line in Magic history. This could only be achieved through the combination of a number of artefacts, combined at exactly the right time, that had been set up by the most cunning bastard in the history of Magic, Urza, over several thousand years. And even after that, he still showed up to scare the next big bad of magic shitless just by his mere presence.
Yawgmoth did not start his life in MTG lore as the ultimate bad guy, rather he was simply known as Yawgmoth, the healer, who was exiled from Dominarian civilization (known as "The Thran" who were standard humans) for "tinkering" a bit too much with his patients, and his methods were a bit too unorthodox for comfort. He was a drifter for a while, continuing his work around goblin and viashino tribes, until he got called back to mainline civilization. He was called back because one of the most important figures in Thran society, Glacian, a master artificer, fell ill. This sickness stumped all the other healers, and eventually Yawgmoth was called back from his exile to fix this man.
What Yawgmoth actually found was that the power source for the entirety of the Thran, the powerstone, was poisoning everyone who was exposed to it. The reason Glacian was so horridly affected as because he got stabbed with a powerstone shard. And so began a gradual process of Yawgmoth obtaining more and more authority in the government of the Thran, manipulating the hell out of whoever didn't agree with him, and even gradual seduction of Glacian's wife, Rebbec.
For the longest time Yawgmoth didn't have his own card, or even know for sure what he looks like. The reason for this anonymity is simple: he would completely break the game if he was added. Remember, this guy was able to kick the shit out multiple planeswalkers from before the mending, at the same time, and is just as powerful as that entails. The natural argument to this is "treat him like another Nicol Bolas, or the Eldrazi Titans," if you think this, you simply are not comprehending how powerful Yawgmoth is.
Nicol Bolas in the current story is simply trying to regain the power he lost in the mending. Yawgmoth massively, MASSIVELY exceeded that power anyway, and was able to just flatly stop the rampage of no fewer than ten pre-mending planeswalkers as they rampaged through his own universe (because he has one of those. Not a pathetic little meditation plane, we're talking Phyrexia here).
In fairness, the Eldrazi Titans at full power could possibly equal his power level, as it is stated that they are at no point at their full power, and even then to kill them it took the power of an entire plane. As they would just be as format warpingly powerful as a Yawgmoth card, there is a VERY good reason they are not represented as such, because if the titans were at their full power, they would break the game (and it kinda already happened, as Emrakul, the Aeons Torn" has been banned from EDH for quite some time).
That said, WotC in 2019 did reveal a Yawgmoth card. Why is it reasonable that this card doesn't break the game? Because it is of him before his apotheosis. MaRo stated we might get more Yawgmoth cards in non-Standard sets, each later in his life than the Yawgmoth card before it. So we might eventually have a card that represents Yawgmoth at his height.
|Planeswalkers of Magic: The Gathering|
|Original Five:|| Ajani Goldmane - Chandra Nalaar|
Garruk Wildspeaker - Jace Beleren - Liliana Vess
|Alara:||Elspeth Tirel - Nicol Bolas - Sarkhan Vol - Tezzeret|
|Zendikar:||Gideon Jura - Nissa Revane - Sorin Markov|
|Scars of Mirrodin:||Karn - Koth of the Hammer - Venser|
|Innistrad:||Tamiyo - Tibalt - Davriel Cane|
|Return to Ravnica:||Domri Rade - Ral Zarek - Vraska|
|Theros:||Ashiok - Kiora - Xenagos - Calix|
|Tarkir:||Ugin - Narset|
|Kaladesh:||Dovin Baan - Saheeli Rai|
|Other:||Dack Fayden - Vivien Reid - Kaya|
|Commander 2014:||Daretti - Freyalise - Nahiri - Ob Nixilis - Teferi|
|Pre-mending:||Bo Levar - Commodore Guff - Jaya Ballard - Urza|
|Planeswalker Groups:||The Gatewatch|