The turtle anecdote has a special meaning to anthropologists. Clifford Geertz uses one version of the story to illustrate a point about both culture and anthropology in his classic essay on thick description. He writes,

There is an Indian story--at least I heard it as an Indian story --about an Englishman who, having been told that the world rested on a platform which rested on the back of an elephant which rested in turn on the back of a turtle, asked (perhaps he was an ethnographer; it is the way they behave), what did the turtle rest on? Another turtle. And that turtle? "Ah, Sahib, after that it is turtles all the way down. (Geertz 1973)

The idea here is that culture is the turtles. When the anthropologist tries to explain a particular belief or value or practice, what she does is reveal a turtle--another belief or value or practice. Beneath that second turtle is third belief or value or practice, and then another, ad infinitum. This isn't to say that interpreting a bit of culture is futile. Indeed, Geertz believes that such interpretation is the heart of the anthropological enterprise. However, the task will never be complete, and an ethnographer will never be able to capture all the meanings involved in a particular bit of culture. Instead, the best she can hope to do is to understand as much as she can about the various ways that belief or value or practice fits into its many contexts. Culture constantly references and builds upon culture.

Most cultural anthropologists (at least in the US) are familiar with this essay, and many have since said or written "turtles all the way down" to express what is now an article of dogma among much of the profession. While an anthropologist can certainly find an important and more or less accurate interpretation of what a bit of culture means, that interpretation will never be complete. There is always room for reinterpretation, argument, and more turtles.

The importance of the turtles to contemporary anthropology is evident in the suspicion of many cultural anthropologists toward sociobiology, evolutionary psychology, cruder forms of economic determinism, and other mechanistic explanations for bits of culture. Simply put, these modes of explanation tend to invoke one and only one turtle, not leaving any room for subsequent reptiles.

Geertz, Clifford
1973 "Thick Description: Toward an Interpretive Theory of Culture." In The Interpretation of Cultures. New York: Basic Books.