This is another interesting therapy style, pioneered by the Australian social worker Michael White (1948-2008).
Here is my condensed account of narrative therapy: the main idea that I appreciate in this style is the application of a "story metaphor" to a person's life and problems. The patient becomes an author. Problems in the person's life (such as depression or eating disorders) become characters, and each of these characters gets a name. These characters are understood to have voices in the narrative, and to influence the story. The ways in which the different characters exert influence upon the story are examined, by the patient and by others. The role of the character--its purpose in the plot, so to speak--is considered. The question is considered of whether the story requires the character in some way, whether the character needs to be present, or what the story would be like without the character at all. The next step is to creatively "re-author" the story, addressing the problems externally as characters to deal with. The motives could be considered about why the different characters are behaving as they do. Elements which empower or weaken the character are considered. Important messages the characters might have to communicate could be considered or validated. The different "antics" of the characters (problems) could be anticipated, "spoken back to", or thwarted, through a creative act of "re-authoring".
The idea is really quite similar to cognitive-behavioural therapy, but perhaps with a more imaginative infusion of literary theory.
I find much of the written theory about this style incredibly cumbersome and laden with unnecessary jargon. Also I think this style, like many others, tended to see the founder as a sort of guru. There is a phenomenon I call the "guru effect" in which people with complex problems report significant change when they encounter some wise, charismatic figure, often in a public setting (I guess we can see this on certain types of TV shows these days).
I don't mean to be too critical of the "guru effect" because I acknowledge that there are some people who can share their charisma and wisdom very effectively, in a way that can be dramatically helpful. The word "guru" itself, and its origins, ought to be treated with respect, and the existence of this phenomenon can be appreciated as a gift to the world.
However, the "guru effect" can sometimes lead to a lot of dogma and a type of religious fervour that can foster overvalued ideas about what it is that is actually helping. This is especially problematic, in my opinion, if the adherents to a particular style begin to reject or criticize other styles or ideas, in ways that are not founded upon good evidence.
In any case, I think there are some imaginative and helpful ideas in narrative therapy--I'm always on the lookout for variations of cognitive-behavioural therapy or other therapies that are a little bit more imaginative, creative, or even fun (therapy isn't always fun, but humour, enjoyment, creativity, and playfulness can be immensely important elements at times).