Levi-Strauss's structural approach to anthropology has been extremely influential. Derived from linguistics theory, structural anthropology attempts to explain human culture in terms of the mental structures that essentially give meaning to, and constrained, human thought and action. Levi-Strauss suggested that the human mind works in binaries like "raw/cooked," "hot/cold," "good/evil," and so on. He interpreted the religious beliefs of his subjects as attempts to resolve these apparently irreconcilable binaries. In short, culture was the product of, or structured by, the collective human mind. This approach to anthropology was very different than a functionalist approach, which tended to analyze different aspects of human culture in light of the role they fulfilled within a society.
Levi-Strauss was influential in another way, as well. Unlike many other anthropologists, who tended to categorize societies along a continuum of civilization and primitivism, he held a deep respect for his subjects, in part because his structural theory acknowledged that their cultural institutions proceeded from the same sources as allegedly civilized people. He makes the point clearly in Tristes Tropiques, one of his most famous (and accessible) books:
We must accept the fact that each society has made a certain choice, within the range of existing human possibilities, and that the various choices cannot be compared to each other: they are all equally valid.
Levi-Strauss goes on to stipulate that is perfectly understandable for Western anthropologists to be shocked by customs such as cannibalism. True objectivity, he claims, comes when a western social scientist realizes that "certain of our own customs might appear, to an observer belonging to a different society, to be similar in nature to cannibalism..." This commitment to objectivity and a non-judgemental approach to anthropology has been highly influential in the field.
Source: Claude Levi-Strauss, Tristes Tropiques (New York: Penguin Books, 1992), 386-389.