An elderly English butler, having received the suggestion that he borrow his new employer's car and 'get out and see the country', decides to go visit a former housekeeper, who worked with him. The reader is initially unsure of their relationship, but a romantic interest is implied (although denied by the narrator.)
Gradually, through his internal thoughts, we begin to see that his stated pride in the traditions of skilled service are a hollow shell, that his former employer was not the paragon of nobility that he had hoped and believed he was, and that he feels his life was likely wasted. He remains unable to engage in regular human interaction, finding even the interactions of other servants with similar backgrounds nearly impossible to understand.
I haven't seen the movie that was made of this book, but it seems a very strange choice for film adaptation, as most of the significant aspects of the novel are in the mind of the main character.
The book however, is an excellent character study, beautifully written. It does remind me of another of Ishiguro's novels, "An Artist of the Floating World." Although the characters in each book are very different from each other, they both deal with a similar sort of self-denial and shame.