The storyline of Anna concerns an amnesiac man who dreams of a sawmill in the mountains near his town. He decides to go there to find out its connection to his missing memories and a woman named "Anna" who seems to be calling out for him, and enters the house by solving puzzles in the garden. He becomes aware that the house is haunted after seeing several strange phenomena.
As the protagonist explores, he begins to hear voices belonging to himself and the eponymous Anna, among others. Through these voices and texts found throughout the sawmill, he discovers that he has had an obsessive history with an ancient deity named Anna that he had since forgotten. However, the plot is ambiguous from this point; one interpretation holds that in times of yore, Anna would lure men into worship, causing them to murder those close to them or starve themselves at the feet of her statue, and after she seduced the protagonist, he murdered his own wife and children for threatening his relationship with Anna. The other interpretation paints the protagonist as the villain, meeting a human avatar of Anna in the forest and falling in love with her. However, after she left because of his obsession with her and abusive personality, he sacrificed children to summon her again.
The game has three main endings; in an inversion of the norm, the more effort that is put into achieving an ending, the less optimistic the conclusion will be. In the first scenario, the protagonist concludes that Anna was burnt as a witch centuries ago and leaves the house, vowing never to return. In the second ending, the protagonist reminisces about Anna, realizes that he cannot live without her, and opens himself up to possession by her, joining the multitude of mannequins that are found throughout the house. In the third ending, the protagonist remembers killing his real wife after she defiled Anna's statue, and finds the statue, along with dolls of his children, in a small chamber. As the tunnel to the chamber caves in, he realizes that he will stay in the chamber forever, but he does not care because he has "Anna" with him.
The plot is ambiguous due to the uncertainty of the protagonist as to whether or not the sawmill is real or merely a dream, as well as the strange phenomena that occur throughout the story and the vague and unconnected nature of the voices.