The woman in black (a.k.a. Jennet Humfrye) is not some friendly Caspar-type ghost. She's not even your typical ghost who wanders through a big old house, weeping and trying to find its way to a better place. Nope. This ghost is angry and filled with vengeance and will not let anyone stand in her way.
The woman in black was once just a young woman who happened to have a child out of wedlock. This being England in the nineteenth century, way before Teen Mom stepped in to destigmatize out-of-wedlock birth, she couldn't exactly run off and raise the child on her own. So, her sister Alice Drablow convinced her to give the child to her and her husband to raise as their own.
Sounds great, right? Jennet keeps her reputation; the barren Drablows get a child; and the kid grows up with two loving, apparently wealthy parents. She even gets to hang around Eel Marsh House to keep an eye on him.
Not so much. Jennet—like a lot of moms strong-armed into adoption—isn't too pleased about having to give up her son. In a letter that Arthur finds, she writes:
He is mine. Why should I not have what is mine? He shall not go to strangers. I shall kill us both before I let him go. (9.36)
Her sister is majorly pressuring her to give up her child, and she only gives him up because she ends up giving in. There's no sense that she wants to give him a different or better life. In fact, in this letter, she sounds like she's lost all control of her life. Her sense of being wronged, and of being a bystander in her own life, only increases after she has to watch her child die—before he ever knows that she's his mother.
Obviously, death isn't going to put an end to anger this strong. After Jennet dies, she continues to haunt the town filled with anger and vengeance. As Daily describes, it, she was:
Mad with grief and mad with anger and a desire for revenge. She blamed her sister who had let them go out that day, though it was no one's fault, the mist comes without warning. (11.113)
Even though Nathaniel's death was no one's fault, Jennet blames everyone. She's alienated. With no friends or family, she develops a Jennet vs. World mentality that just ends up destroying everyone in her path. Like Arthur.
Arthur comes across her by accident, but attracts all of her ire when he continues to poke into the affairs that are still so painful to her. Because, Jennet never had a chance at happiness, she makes a living (so to speak) from taking away other peoples' happiness.
That is exactly what she does to Arthur at the end when she destroys his happy family—something that she never had a chance to have. Is it random? Yeah, it's a little random. Arthur never did anything to her. He doesn't even live in the village. But Nathaniel's accident was random, too, and to Jennet, everything is connected. Arthur's happiness is directly tied to her misery. And so she destroys him. The past reaches out to haunt the present, even if it's not the present's past.