The director of this film, Alexander Sokurov, is famous for his complete disregard for commercial success and his determination to make films the way he wants them made. The narrative structure of his films is usually very loose. For some fans, (but by no means all) he is considered to be an heir to the great Andrei Tarkovsky.
He's one of the most highly regarded contemporary Russian filmmakers. This film opens Sokurov's trilogy that includes Krug Vtoroy (The Second Circle), Kamen (The Stone) and Tikhiye Stranitsy (Whispering Pages). Krug Vtoroy is about the absence of connections between people and the mechanical insertion of once-important rituals into their lives.
In the story, a young man (Petr Alexandrov) shares a dingy apartment with his father, who has had the poor judgement to die on a weekend. Because of this, the son has to keep his father's body in the house, since undertakers don't work on weekends. This gives him an opportunity to consider his father's death and the human situation at close hand.
In this film, the corpse gets to consider the son, as well. The young man has difficulty raising the tiny amount he needs to give to the undertaker to get him to take his father's body away for burial, but finally succeeds in this.