Turtles all the Way Down is a vivid metaphor for Infinite Regress: the feeling that every explanation depends on a deeper explanation, and that the chain never reaches a final ground. The image comes from a cosmological joke-story: the world rests on a giant turtle, which rests on another turtle, and so on “all the way down” - wikipedia 
The phrase is popular because it turns an abstract philosophical problem into a picture you can’t unsee. If you keep asking “what supports that”, you either decide there is a bottom turtle (a foundation), or you accept a bottomless stack (an endless regress), or you change the rules of the question and say the whole stack is the wrong model.
In philosophy, the turtle stack shows up most often in arguments about knowledge and justification. If every belief needs a prior reason, and every reason needs a prior reason, when do you stop and say “this is enough”. Different traditions answer differently: some want Foundationalism (a base), some prefer Coherentism (a web), some accept Infinitism (no end), and some treat “stopping points” as practical commitments rather than metaphysical discoveries.
The story also became a modern science-pop trope through Stephen Hawking’s use of it near the opening of A Brief History of Time, where it frames the temptation to treat “ultimate explanation” as an infinite tower of supports - penguinrandomhouse.ca
Outside philosophy and physics, “turtles” has become a shorthand for recursion in culture and computing: layers built on layers, frameworks built on frameworks, meta-comments stacked on meta-comments. Sometimes it is affectionate (a wink at complexity), and sometimes it is a warning (a smell test for systems that never cash out into something checkable).
The phrase also lives a second life as a title. John Green’s 2017 novel *Turtles All the Way Down* repurposes the metaphor to describe spiralling thought and looping anxiety: not the universe resting on turtles, but a mind that can’t stop stepping down into its own justifications and fears - wikipedia
# See - Infinite Regress and Recursion - Foundationalism and Coherentism - Infinitism and Epistemology - Cosmology and A Brief History of Time - Metaphor and Hard Problem