It doesn't really matter what you know her as. Even if you have never heard of the Mother of Demons, Dawn of Doom or Madam Satan. Chances are, you have in fact, heard the name Lilith before. Yes, it is that Lilith. The first woman who was the wife of Adam, before she was banished because she refused to submit to him. This led to her time spent in the waselands outside of Eden for an extended period of time where all seemed helpless. Little did she know that soon, her life would be turned upside down. Literally.
Just as all hope seemed lost and the woman had resigned to her very likely fate of having to wander the wastelands for all eternity, that all changed in the blink of an eye. Especially as she encountered none other than Lucifer Morningstar. An angel who just like her, had been banished from the only home he ever knew. Helping him and healing the wounds left where his wings had been ripped from his back, she was quick to become his ally. Naming herself Madam Satan to honor him as she remained by his side.
Besides the first woman, Lilith is also known to be the first witch. Meaning all of witch kind that is alive today, thank their existence to her. Whether that is due to her sharing her knowledge or a bloodline with them is unknown. However, taken into consideration she also carries the title of Mother of Demons while not being responsible for their creation, insinuates it might've been the former. Regardless, she is one Hell of a woman (pun intended) and a force to be reckoned with. Showing us that there's no shortage of powerful women in this show.
Initially sent to Greendale in order to serve as some kind of mentor for Sabrina by Lucifer himself, Lilith couldn't exactly infiltrate the place as Madam Satan herself. Instead, she did what any morally grey character would do and disposed of the high school teacher, Mary Wardwell. Taking her place, made it a lot easier to get close to Sabrina in an attempt to corrupt her and tempt her into signing the Book of the Beast.
Eventually found out, Lilith is then faced with a difficult decision. One that will send her into a different direction entirely as she has long grown sick and tired of Lucifers misogynistic ways. Instead, she allies herself with the Spellmans and the witches in Greendale to take down the man once and for all. Having tried for centuries to get Lucifer to marry her so she could become the very Queen of Hell, she only manages to achieve this feat as regent until the Devil's rightful heir comes of age.
While seemingly having a preference for Mary Wardwell when it comes to her physical appearance, Madam Satan's true human form is that of a teenage girl. She has a sickly pale looking skin, hair that's an absolute mess and clothes that finish the entire appearance. Her demonic form on the other hand, has green skin, no nose, deeply sunken black eyes and teeth that are pointed and sharp. As for her personality.. that's a whole other can of worms!
It should come as no surprise there's a lot of depth to a character such as Madam Satan. Having lived for many thousands of years, she doesn't really seem to have the moral compass one would expect of someone who served the Dark Lord for as long as she has. One should note however, that her every action serves nothing else but her own plans. Even if at times, it may seem as if she's actually aiding another with no benefit to herself. She's a master at making people believe she's nurturing and caring, but is actually quite the opposite.
An expert at manipulation, Madam Satan stops at absolutely nothing to get what she wants. While we may question her way of going about things, she often times does have a good (enough) reason for them. Thus not even questioning the crimes she commits. However, at the same time she shows she's capable of change as she allies with Sabrina and actually grows to respect the teenager. Giving her a tremendous amount of growth as a person throughout the show.
As both a witch and a demon, it's not surprising Lilith possesses a wide variety of abilities. Her dark witchcraft being the most defining trait by far. On top of that, she's capable of telekinesis, shapeshifting and necromancy. Possessing the ability to spy using mirrors, dream walk and poppet puppetry to manipulate events, she's a well rounded force to be reckoned with and one you wouldn't want to cross.