The whole book-the whole four volumes, actually-is structured according to a complex musical metaphor, and the Overture to The Raw and the Cooked explicates this metaphor in detail. You'll need to know something about serialism (i.e. Schoenberg) to understand it, but once you do you'll really begin to see what Lévi-Strauss is up to. He thinks that myth is not like poetry, and is more like music than ordinary language. I think his comparison is misguided, based on a misunderstanding of serialism, but it's essential to understand why he correlates myth and music to understand the project.

In the main part of the book, he goes on to select a "key myth," a somewhat arbitrarily-chosen tale from the Bororo, a people he has studied fairly intensively (and did some fieldwork among). He then begins a massive project of connecting this myth to other myths from South America, breaking down and analyzing all the little bits and pieces as he goes. The logic can be hard to follow at times; his little diagrams don't help much, and in fact he seems to see this and ditches them in later volumes. But if you lose the thread, you can lose track of the whole book.

Ultimately, he's going to link up a thousand-odd myths from both Americas, demonstrating how each transforms and adds to other themes, until we get a vast complex of American mythical thought laid out in a mesmerizing sort of crystalline web of relations.

In short, Lévi-Strauss thinks that myths are a way of thinking, using concrete objects, about such problems as self and other, social relations, kinship, cooking, culture and nature, and so forth. He argues that each myth demonstrates a particular thinking-through of such problems by what amounts to cultures as intellectual entities. This may seem hard to believe, but if you've read The Savage Mind, this is the bricoleur at work.  

 Warning:  Not for Normal People

From Decameron Web: 

 In anthropological terms the concept of "the raw" verses "the cooked" has long been associated with the dichotomy between the natural world and the world of human culture. In a broad-based empirical study of native mythologies, Claude Lévi-Strauss proposes a structural and thematic link between the opposition of the raw and the cooked in mythological thought and man's attempt to establish a balanced relationship between natural and cultural forces.

Lévi-Strauss postulates that the raw/cooked axis is characteristic of all human culture, with elements falling along the "raw" side of the axis being those of "natural" origin, and those on the "cooked" side being of "cultural" origin - i.e. products of human creation. Symbolically, cooking marks the transition from nature to culture, by means of which the human state can be defined in accordance with all its attributes. In mythological thought, the cooking of food is, in effect, a form of mediation between nature and society, between life and death, and between heaven and earth. The cook, in turn, can be viewed as a cultural agent whose function is to "mediate the conjunction of the raw product and the human consumer," the operation of which has the effect of "making sure the natural is at once cooked andsocialized."

OK..... We are talking about the universal tension between Culture and Nature. Before people (those few that have made it this far) get too worked up about the seeming tortured prose, remember that this was written in French.

"The English translation of Le cru et le cuit by Claude Lévi-Strauss, is not incorrect, but it is perhaps incomplete. "Cuit" in French does not necessarily mean "cooked", but is also used to denote "done" , which is not necessarily obtained by cooking. In this case, Strauss' use of cuit implies what culture and society do to the raw and make it 'done' or 'cooked'."

Therefore, The "Culture <----> Nature spectrum is connected by cooking,but by being "done."Man mediates nature by socializiation -- and in the caseof food, cooking turns the raw into a social artifact.So, continuing on: 

"Similarly the male "seducer" is a man who is in mythological thought considered to be devoid of social status with respect to his behavior. He is viewed as acting only in accordance with his natural properties - physical beauty and sexual potency - in order to subvert the social order of marriage. His actions, in effect, de-socialize (or un-cook) the woman he seduces. Thus, both "poison" and the "seducer" are natural elements with properties that allow for an "interpenetration" of nature and culture that is at once destabilizing and dangerous.In the fourth day of the Decameron the reader is presented with two tragic love stories in which a young woman is presented with the heart of her dead lover - one heart is presented "raw" and the other "cooked" (IV, 1 and IV, 9). In the case of the "raw" heart, the woman performs an almost ritualistic act of mourning over the object, bathing it with her tears and a vial of poison from which she prepares herself a fatal draft. Her choice to utilize the poison to join her lover (a "seducer") in death can be viewed as a rejection of the cultural for the natural on her part. The poison becomes the medium which allows her to "un-cook" and "de-socialize" herself. In the story of the "cooked" heart, on the other hand, the woman is unaware of her lover's death. It is her husband who discovers his betrayal, kills the lover, and orders the man's heart to be cooked and served to his wife. The husband effectively "cooks" the seducer of his wife, thus neutralizing his "natural", socially subversive qualities. The wife, on the other hand, is able to "eat" her lover only because he has been "cooked", and therefore "socialized." And since eating cooked foods is a cultural act, she has unwittingly assimilated the social order, effectively eliminating any "point of isomorphic coincidence" between herself and her lover, or between nature and culture. Once her is transgression revealed, she loses her social status and now has no where left to turn. Her death, in relation to the "cooked" heart, represents the triumph of culture over nature."