Simply: theory of the narrative.
Narratology is a method of literary criticism in the vein of structural exegesis, in which the critic attempts to analyse plot structure and prose form for insights into the nature and meaning of a literary work. One of the chief theorists of narratology, Claude Lévi-Strauss, asserted that there are specific universal patterns of narration, which can be studied and compared to each other. The fundamental belief at work is that the narrative mode is one of the most basic ways in which humans fashion their perceptions of the universe. In this way it is closely related to Formalism and Structuralism.
Some history
A milestone in the development of the narratological method was the observation that narratives can be found throughout the history of human communication in a variety of forms; oral and written language (in prose or in verse), of course, but also sign languages, still or moving pictures (as in narrative paintings, stained-glass windows, or films), gestures, music, or comic strips). Because the stories 'told' in any of these forms can be translated into nearly any other form (as in film re-makes of books, or poetic retelling of fairy tales), the narrative structure presumably should be considered and studied independently from the medium. This is a major tenet of narratology.
The term "narratology" is a translation of the French term narratologie--introduced by Tzvetan Todorov in Grammaire du Décaméron (1969). Todorov does not explicitly eliminate the study of narrating from the "science of narrative" he envisions; but his examination of Giovanni Boccaccio's tales focuses rather more heavily on the narrated, and his goal is to develop a grammar to properly describe it. Thus, this has diverted the path of narratology from that of structuralism and its ilk.
Claude Lévi-Strauss is the author of Structural Anthropology. In that he conducted a narrative study of myth, and concluded that it always involves the transformation of one set of semantic oppositions into another, less radical one through a mediation or a series of mediations. Thus he endeavored to shed light onto the entity of myth itself, as a mode of human narration of universal structures.
Vladimir Propp wrote Morphology of the Folktale, a shining example of narratological interest. He studied a multitude of Russian fairy tales, and devloped a complex description of many of the diverse components of what was narrated in each of the tales. Through this he came up with the notion of function or category of actions considered from the point of view of their basic meaning in the tale where they appear. In the end he specifically isolated and recorded 31 functions that constitute the fundamental elements of (Russian) fairy tales. He asserted that every single tale (perhaps all stories) contain the function (for example) of either lack (of home, of wife, of gold) or villainy, and proceeded to another appropiate function as denouement: rescue or wedding. Propp also isolated seven basic roles assumed by characters in (fairy) tales, seven dramatis personae each of which corresponds to a particular "sphere of action" or "set of functions": the hero (seeker or victim), the villain, the princess (a sought-for person) and her father, the dispatcher, the donor, the helper, and the false hero.
Some Deficiencies
The most obvious (and perhaps therefore well-founded) attack on Narratology is that it is a reductive method, and leaves out too much valuable data from interpretation. It is also argued that the Narratologist's description (PRopp's functions) are far too static to capture the very dynamics that the form of criticism claims to study. Recent criticism, accordingly, has tried to work out more fluid language, such as musical terms, and has devloped a more complex system. Thirdly, there is the critique that Narratology is blind to the pragmatics, the context, of a story, which many argue have definite importance on the structure and its developments. Finally, there are those that accuse narratology of depending on a type of double logic. That is, that narratologists in turn rely on opposing principles to make their arguments. One principle emphasizes the primacy of event over meaning, that is, insists upon event as the origin of meaning; the other stresses the primacy of meaning and its requirements, that is, insists upon event as the effect of a will to meaning. It is very difficult to logically synthesize these principles, and this argument alone might be a reason why narratology wiill never be able to prvide completely a satisfactory account of a narrative.
More proof we need all the forms of literary criticism to approach a complete interpretation.
Once again: leisure, school and site: http://www.press.jhu.edu/books/hopkins_guide_to_literary_theory/narratology.html