Turtles all the way down refers to a myth about the nature of the universe (see Cosmology). Stephen Hawking in his 1988 book A Brief History of Time starts with an anecdote about an encounter between a scientist and an "old lady."
A well-known scientist (some say it was Bertrand Russell) once gave a public lecture on astronomy. He described how the Earth orbits around the sun and how the sun, in turn, orbits around the centre of a vast collection of stars called our galaxy.
At the end of the lecture, a little old lady at the back of the room got up and said: "What you have told us is rubbish. The world is really a flat plate supported on the back of a giant tortoise."
The scientist gave a superior smile before replying, "What is the tortoise standing on?"
"You're very clever, young man, very clever," said the old lady. "But it's turtles all the way down."
The anecdote in this form has achieved the status of an urban legend on the internet, as there are numerous versions in which the name of the scientist varies (e.g., Thomas Huxley, William James, Arthur Stanley Eddington, or Carl Sagan) although the rest is the same.