While the game's name is Catherine, the main character is actually a 32-year-old salaryman named Vincent (voiced by Koichi Yamadera). Catherine (voiced by Miyuki Sawashiro) is a stylish 22-year-old girl who apparently has the charms of a young girl.
The game begins when Vincent, a vegetarian who has no ambition in work or love (I'm not sure if he's literally a "vegetarian," or if the term "vegetarian" is some sort of metaphor for his personality) runs into the mysterious Catherine one day. At night, he has nightmares.
The nightmares serve as an action component for the game. Set in a world with an unending stairway, Vincent has to make it to the top of the stairs, or he will not be able to awaken.