Who is she?
Again, another vague backstory. At the least the novel implies that she probably was formerly human prior to her coming to rule the Other World. She is a wicked temptress who spies on children and offers them a "better life" if they chose to remain in the Other World after she gave them their heart's desire. However, this is a trap to which she has the children sew buttons into their eyes and she steals their souls. She probably also eats them. Maybe.
She had done this to three children prior to her meeting Coraline Jones when she and her parents move to the Pink Palace Apartments. She discovers a doll version of herself and ends up finding a small door that led her to the entrance of the Other World. Slowly but surely, the Beldam (or Other Mother) bends things to make Coraline want to stay. But then she tries to have her sew buttons into her eyes. Just like all the others.
At first, the Beldam plays the role of the seemingly perfect mother. She gives Coraline attention and sells the Other World as being the best thing. However, underneath that is a self-serving authoritarian. She claims to "love" the children she lures into the Other World, but it is really just a farce: she feeds off the lives of the children and ultimately discards them in the way that a child does a broken toy. In other words, if she grew bored with them, she would lock them away where they eventually die. Ultimately, she views the children and her creations as objects that are suspect to being disposed of.
She also has something of a sadistic streak as demonstrated with her horrific abuse of her creations such as abominating the Other Father and then forcing him to attack Coraline against his will, or stitching the Other Wybie's mouth shut and then gruesomely kills him for assisting Coraline.
The Beldam also loves games playing one with Coraline saying that if she received the eyes of the ghost children, she'd allow her to leave while noticeably not shaking Coraline's hand to seal the deal. Of course as most villains do, she cheats during the game...all while deriding Coraline for cheating. She goes through drastic lengths of trying to obtain Coraline's soul until the world itself starts to crumble around her.
She looks like a perfect replica of Coraline's real mother though without the neckbrace and a more healthy skin tone. The obvious difference are of course the black buttons. As she starts to deteriorate, she takes on a more skeletal form until she gains spider-like attributes. Hm...a mysterious being who is able to warp reality and lures children into her world...and she has spidery traits. Sounds familiar.
Powers and Abilities
She has near-omnipotence over the Other World where she can manipulate it into whatever she wanted. Additionally, she is able to control the weather. But this largely depends on how much energy she has and once she becomes weakened, the world starts to revert back to its deteriorating state.
Shapeshifting is another power she has first appearing as a near-perfect replica of Coraline's mother before transforming into a more skeletal appearance. But there is the implication that she can take on any appearance, but then again, looks like it depends on how much energy she has.
However, her main weakness is her inability to create things out of scratch but merely replicate whatever already existed thus giving her limitations.