Thomasin
Anya Taylor-Joy is Thomasin, the teenaged daughter of farmers William and Katherine and the protagonist of the film. After her parents were kicked out of an organized Puritan settlement because of a disagreement over religion, William and Katherine moved their family -- including Thomasin -- to a remote area in New England. Thomasin was used to being near people and missed the hustle and bustle of the settlement. She was heartbroken to leave the place she had so clearly grown fond of.
Thomasin is a passionate and headstrong young woman who is deeply curious about the world around her. Along with her brother, she ventures into the woods with her younger brother Caleb, whom she lovingly consoles about the death of their brother.
Eventually, Thomasin becomes consumed with the witch and her magic, killing her mother and succumbing to the influence from the witch and her coven. Though she is intelligent and generally well-meaning, Thomasin is easily influenced by the people around her, setting the film's events in motion.
The witch
The specter of the nameless, faceless witch at the center of the film hangs heavy over Thomasin and her family. The witch is a rapacious, violent, and uncaring person who becomes consumed with enriching her life -- typically at the expense of others. Her depravity is matched only by her desire to control Thomasin and add another member to her coven.
William
William is Thomasin's father and the fierce and intelligent patriarch of their family. A headstrong and boisterous man, he stood up for what he thought was right and got his family kicked out of their Puritan colony. Despite his belief in Christ, he did not adhere to the same dogmatic ways of thinking as everyone else, instead forging his own path forwards towards salvation. However, in ignoring the covenants of his religion and community, he didn't stop to consider what effect his actions could have on his wife and children.
However, William is devoted to his family. He sought to raise his children up as productive, resourceful, and contributing members of society. And he went to extensive lengths to achieve that -- including locking his children in the family's goat pen to teach them a lesson.
Katherine
After the kidnapping and death of her infant son, Samuel, Katherine is bereft. Inconsolable and deeply depressed, she ponders how Samuel could have died and why her family is experiencing profound grief and discomfort. Why has a seemingly omnipotent force targeted them? And perhaps most importantly, how can she stop it from happening. However, just as she finally starts to understand what has happened to her family, more of her children are injured, sending her into psychosis and ultimately resulting in her death.
