The film is set around the turn of the century – not the recent one but the Victorian/Edwardian one. Radcliffe plays Arthur Kipps – a winking reference to the H.G. Wells hero, maybe? – a young lawyer whose once-promising career has been sinking ever since his beloved wife died in childbirth. He has never recovered from his grief: The first thing we learn is that he's suicidal and only keeps going on for the sake of the above-mentioned 4-year-old.
His long-dissatisfied employer gives him a final chance to save his job: He must go from London to the remote Yorkshire village of Crythin Gifford and straighten out the papers of an old woman who died without friends or heirs. On the train, he strikes up an acquaintance with the affable, well-to-do Sam Daily (Ciarán Hinds). Sam will be the last affable face – spectral or live – he sees for the rest of the movie.
The rest of the villagers are downright hostile and try to prevent him from going to the ominous-looking Eel Marsh House, which is cut off from the mainland during high tide. As everyone other than Arthur and Sam knows, Eel Marsh House is haunted by a vengeful spirit, a woman in – you guessed it – black. The mere fact of Arthur's presence seems to provoke her into murdering people in the village. (The mechanism here is central to the story and is never quite clear. It's as though Arthur is somehow bringing her back with him from the house – or something.)